Department of Physics
MASTER’S THESIS
Collateral Optimization
Johanna Bylund August 2017
Supervisor: Johan Sundberg, Cinnober Financial Technology, Ume˚a Examiner: Martin Rosvall, Department of Physics, Ume˚a University
Master’s Thesis, Engineering Physics, Ume˚a University.
Johanna Bylund, joby0026@student.umu.se
Supervisor: Johan Sundberg, Cinnober Financial Technology.
Examiner: Martin Rosvall, Department of Physics, Ume˚a University.
The financial crisis in 2008 has led to regulations and increased demand for high-quality collaterals, which has forced many financial institutions, such as dealer banks, to improve their collateral managing techniques. Optimizing the collateral pool in a dealer bank is known as Collateral Optimization.
However, not all banks and financial institutions use and manage their collateral portfolios in an optimal way, which can lead to unnecessary costs. Banks can prevent this problem by investing in a system that optimizes the collateral allocation or transforms to higher valued collateral. In this thesis, we describe the basics of such a system in the case where a bank clears trades by several clearinghouses with different collateral demands, constraints, and margin requirements. Therefore, the system must allocate collateral in various ways to cover the risk margin at the different clearinghouses. We present a Java implementation that takes as input collateral properties such as valuation, cost, type, risk, and quality and outputs collateral quantity to cover risk margin. As constraints, the underlying model takes clearinghouse requirements and collateral valuation, and a user can choose between two different linear programming optimization methods, Simplex method and Branch and Bound. When using the Simplex method, the user is either given a way to allocate the existing collateral or a suggestion for how to transform to achieve a better solution. The Branch and Bound method always finds the optimal collateral allocation and the optimal solution when collateral is missing. Besides proposing an approach, we have examined other ways to look at collateral preference, cost and allocation, because there is no right answer to the question on how to manage collateral, and every institution may need an individual solution.
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Finanskrisen 2008 gav upphov till regelverk som i sin tur ledde till ¨okad efterfr˚agan p˚a finansiella s¨akerheter med h¨og kvalit´e. Detta har tvingat m˚anga finansinstitut, s˚asom kommersiella banker, att f¨orb¨attra hanteringen av s¨akerheter. Att optimera anv¨andningen av s¨akerheter kallas Collateral Optimiztion. Detta ¨ar n˚agot som inte alla banker och finansinstitut g¨or p˚a ett optimalt s¨att, vilket kan leda till o¨onskade kostnader. Detta kan dock f¨orhindras genom att investera i ett system som optimerar anv¨andningen av s¨akerheterna eller omvandlar existerande s¨akerheter till h¨ogre v¨arderade.
I denna rapport beskriver vi grunderna f¨or ett s˚adant system i det fall en bank clearar handel hos flera clearinghus med olika krav, begr¨ansningar och riskmarginaler. Detta g¨or att systemet m˚aste f¨ordela s¨akerheter p˚a olika s¨att f¨or att t¨acka riskmarginalen vid de olika clearinghusen. Arbetet resluterar i en Java-implementation med inputparametrar som r¨or de finansiella s¨akerheternas v¨ardering, kostnad, typ, risk och kvalitet d¨ar kvantiteten f¨or varje s¨akerhet ¨ar det som modellen resulterar i. Som begr¨an- sningar anv¨ander sig den underliggande modellen av clearinghusens krav och v¨ardering av s¨akerheterna, d¨ar anv¨andaren av systemet kan v¨alja mellan tv˚a olika linj¨ara programmeringsoptimeringsmetoder, Simplex-metoden och Branch and Bound. N¨ar Simplex-metoden anv¨ands f˚ar anv¨andaren antingen ett s¨att att allokera de befintliga s¨akerheterna eller ett f¨orslag p˚a hur man omvandlar dessa f¨or att uppn˚a en b¨attre l¨osning. Branch och Bound-metoden finner alltid den optimala s¨akerhetsallokeringen och den optimala l¨osningen i det fall d¨ar finansiella s¨akerheter saknas. F¨orutom att f¨oresl˚a ett tillv¨agag˚angss¨att har vi granskat andra s¨att att titta p˚a s¨akerhetspreferenser, kostnader och allokering, vilket har gjorts p˚a grund av att det inte finns n˚agot r¨att svar p˚a fr˚agan om hur man optimerar finansiella s¨akerheter, och varje institution beh¨over en individuell l¨osning.
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1 Introduction 1
1.1 Background . . . 1
1.1.1 Collateral optimization . . . 3
1.2 Aim . . . 3
1.3 Goal . . . 4
1.4 Limitations . . . 4
1.5 Disposition . . . 5
2 Theory 6 2.1 Collateral . . . 6
2.1.1 Credit quality rating . . . 6
2.1.2 Collateral markets . . . 7
2.1.2.1 Repurchasing agreement (Repo) . . . 7
2.1.2.2 Securities Lending . . . 8
2.1.2.3 The derivatives market . . . 8
2.1.2.3.1 Exchange-traded derivatives . . . 9
2.1.2.3.2 Over-the-counter derivatives . . . 9
2.1.3 Legal agreement . . . 10
2.1.4 Regulation . . . 10
2.2 Collateral management . . . 12
2.2.1 Collateral transformation . . . 13
2.2.2 Centralized clearing . . . 15
2.2.2.1 Risks of Central Clearing . . . 15
2.2.2.2 Requirements and constraints . . . 16
2.2.2.2.1 Initial margin and Variation margin . . . 16
2.2.2.2.2 Haircut . . . 16
2.2.2.2.3 Credit quality . . . 17
2.2.2.2.4 Lower and upper concentration limits . . . 17
2.2.2.3 Central counterparty charges . . . 17
2.2.3 Collateral cost model . . . 18
2.2.3.1 Funding costs . . . 18
2.2.3.2 Additional costs . . . 19
2.2.3.2.1 Transaction cost analysis . . . 20
2.2.3.2.2 Custodial Fees and Safekeeping Fees . . . 22
2.2.4 Risk management . . . 22
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2.2.4.1 Volatility . . . 23
2.2.4.1.1 GARCH(1,1) . . . 23
2.2.4.1.2 EGARCH(1,1) . . . 24
2.2.4.2 Value at Risk . . . 24
2.2.4.3 Liquidity Adjusted Value at Risk . . . 24
2.2.4.4 Probability of default . . . 25
2.2.4.5 Exposure at default . . . 25
2.2.4.6 Loss given default . . . 25
2.2.4.7 Expected loss . . . 25
2.3 Collateral Optimization . . . 26
2.3.1 Optimizing cost models . . . 26
2.3.1.1 Preference ranking . . . 26
2.3.1.2 Market based ranking . . . 27
2.3.1.3 Economic based ranking . . . 27
2.3.2 Allocation . . . 28
2.3.2.1 Waterfall allocation . . . 28
2.3.2.2 Numerical optimization . . . 28
2.4 Operational research . . . 29
2.4.1 Linear programming . . . 30
2.4.1.1 Simplex method . . . 30
2.4.2 Integer linear programming . . . 33
2.4.2.1 Branch and bound algorithm . . . 33
3 Method 37 3.1 Collateral Optimization model . . . 37
3.1.1 Input Data . . . 40
3.1.1.1 Collateral valuation . . . 43
3.1.1.2 Clearinghouse . . . 45
3.1.2 Mixed integer linear problem . . . 45
3.1.2.1 Mathematical optimization problem . . . 45
3.2 Output . . . 47
3.3 Software implementation . . . 47
4 Results 48 4.1 Ranking system . . . 48
4.2 Collateral allocation methods . . . 49
4.2.1 Simplex method . . . 49
4.2.2 Branch and Bound . . . 49
4.2.3 Analyzing the different methods . . . 49
4.3 Collateral Optimization model . . . 50
5 Discussion 51 5.1 Conclusion . . . 52
5.2 Future work . . . 53
A Test cases - Revised Simplex method I A.1 Case 1 . . . VI A.2 Case 2 . . . VII A.3 Case 3 . . . VIII A.4 Case 4 . . . IX A.5 Case 5 . . . X A.6 Case 6 . . . XI A.7 Case 7 . . . XII
B Test cases - Branch & Bound XIII
B.1 Case 1 . . . XVII B.2 Case 2 . . . XVIII B.3 Case 3 . . . XIX B.4 Case 4 . . . XX B.5 Case 5 . . . XXI
C Result - Tables XXII
C.1 Revised Simplex method . . . XXIII C.2 Branch and Bound . . . XXXI
Introduction
Cinnober creates financial solutions to different kinds of financial parties, such as clearinghouses and banks. A clearinghouse is a financial institution where one of its main function is to act as a central counterparty (CCP), i.e handle the risk of a financial contract written between a buying and selling part, later also called clearing members. If something unexpected were to happen, and one of the parties goes into default, the clearinghouse will guarantee that the obligations of the contract will be fulfilled. To do this the clearinghouse needs resources, which are gathered by demanding collateral deposits from every clearing member. There are many different types of collateral, and since every clearinghouse have different demands and requirements on these and every clearing member can be connected to several clearinghouses, the optimization of the internal mix and usage of collateral for a clearing member is of interest in order to use the collateral resourcefully.
This can be done in several different ways, however, the research on this are mainly done by finan- cial institutions or companies selling a collateral optimization solution to financial institutions. Every institution wants the best solution possible and needs this solution to be protected from the competi- tion, which leads to a low amount of published solutions. Due to this lack of public information, the optimization approach may not be obvious and this thesis is written in order to diminish this gap of knowledge.In this thesis the essential parts needed to optimize a collateral portfolio are established by investigating the internal optimization of collateral usages in a dealer bank that have contracts cleared at several clearinghouses. Using this information, the main factors are determined and used to create a mathematical model that can be optimized by using an operational research technique.
1.1 Background
In finance and banking, clearing is the process of all activities from the time a financial contract is entered until it is settled, i.e. at the time the securities to fulfill the contractual obligations are delivered.
In the market there are several market participants, here called parties, that can trade with each other.
If party P 1 enter a contract to exchange financial flows with a party P 2, the trade is registered between the counterparties as illustrated in Figure 1.1.
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P1 P2 B A
Figure 1.1 – The figure illustrates the flow of assets between two parties P 1 and P 2 where A and B are the units of assets.
In a more real-life example each party have several counterparties and by this, several contract agree- ments to fulfill. This can be rather messy, but the parties can handle and sort this by processing the payment by themselves through bilateral netting. The downside with this is that each party still suffer from the counterparty risk. The solution could be to use a clearinghouse acting as a central counterparty (CCP).
P3
P4 P1
P2
P1 P3
P4 P2
P1 CCP P3
P4 P2
31
7 5
8
3
12 3
4 7
20 12
5
8
15 3
8 5 6
2
7 14
Figure 1.2 – From left, an example of a network of parties that have engaged in a trade can be seen, and at some fixed time transfers different units of assets to each other. The middle picture describes how the network looks when applying bilateral netting, and the right depicts the network of using a central counterparty as an intermediate.
The clearinghouse is a financial institution that take the opposite position of each side of a trade, acting as an intermediate and standing between two counterparties that are connected to the clearing- house. These counterparties, also called clearing members, uses the clearinghouse in order to reduce the risk that one of these will default, or in any other way, fail to honor its trade settlement obligations.
This means that the clearinghouse are responsible for the contract, and the clearing members expects that all transactions will be fulfilled. In many cases, the clearing members are obligated to use the clearinghouse due to regulatory demands. As can be seen in Figure 1.2, the initial trades between the parties are simplified to one trade per party, with the clearinghouse in the middle.
To be able to fulfill obligations that a clearing member can’t, the clearinghouse requires the clearing members to hold margin to cover unsettled positions. This margin is also described as collateral deposits. Its crucial that the amount are correct considering that the clearinghouse don’t want the members to pay too much and risk to loose the member to another clearinghouse, and it don’t want to be in a position where it can’t fulfill its obligations. It is the clearinghouses responsibility to monitor the margin levels and make sure that it covers the outstanding trades. Here, collateral can be whatever a clearinghouse can convert to cash on short notice and with low liquidity risk. The most usual types of collateral are cash, government bonds, corporate bonds, bank guarantees and equities.
1.1.1 Collateral optimization
Cinnober has a system for clearing of financial transactions, TRADExpressTM RealTime Clearing that is used by clearinghouses, inserting itself as the counterparty to both the buyer and seller. Cinnober is also currently in the process of exploring Client Clearing, a back-office system targeted for banks that are connected to several clearinghouses, which is the outset of this thesis. In this case it is interesting to emulate several of the clearinghouses processes of covering risk and optimize the banks total collateral requirements against all of its connected clearinghouses.
Considering a case where a financial institution, party P 1, have contracts that are cleared at several different clearinghouses (see Figure 1.3), where each clearinghouse have different collateral requirements and calculates the risk margin value for each contract differently. This means that P 1 needs to have a pool of different types of collateral, later also called a collateral portfolio. The issue here is to use the existing collateral in the best way possible, and finding a good allocation process to cover the risk values in the most efficient way.
P1 CCP1 (cash)
CCP2 (bonds)
CCP3 (equities) CCP4
(cash)
Figure 1.3 – The figure describes a simplified example of how it can look when a financial institution P 1 trades at four clearinghouses CCP 1, CCP 2, CCP 3 and CCP 4. Every clearinghouse demands different types of collateral to cover the risk associated with the trades.
1.2 Aim
The term collateral optimization includes all actions done by a financial institution to make a more effective use of its existing portfolio of collateral assets. The aim of this thesis is to investigate how a financial institution can optimize the collateral mix in this portfolio, that are used to cover the risk margin value of a contract cleared through a central counterpart. The research regarding this is mainly done by financial institutions where there are barely any public research published, which is one of the factors that contribute to the fact that the solution to the collateral optimization problem isn’t very obvious.
A common fact of collateral optimization is that one of its purpose is to survey the use of collateral and manage the risks in a more efficient way. This can in turn lead to lower funding costs of collateral, and by this, give higher profits. Also, optimizing the collateral usage may boost an institution’s ability to attract extra liquidity, and lower the need for costly and potentially risky collateral transformation services. [1]
A condition for collateral optimization is that the financial institutions, in this case a bank, have good understanding about their existing collateral, including knowledge of the cost, use and settle- ment procedures for each collateral. In order to optimize the collateral usage, the portfolio allocation of the collateral could be improved by considering the requirements and demands of the connected clearinghouses and improving the effective parts that the market controls. [1]
To summarize, one can say that the parameters that controls the optimization of collateral are
• Collateral requirements
• Collateral positions
• Settlement procedures
• Collateral costs.
In this thesis, these factors are studied and elaborated to identify the importance in a collateral optimization model.
1.3 Goal
The goal of this thesis is to determine the factors that affect collateral optimization, create a mathe- matical model and use an operational research technique/algorithm to solve the collateral optimization problem. To do this, one needs to present tools and guidance on how to manage and optimize the internal collateral portfolio of a financial institution. The main goal of these tools is to minimize the cost of collateral, maximize the funding and/or liquidity capacity of the collateral inventory and mini- mize the funding costs.Another goal is to automate the allocation process which is solved by using an operational research algorithm on the created mathematical model, where it all will be implemented in Java.
1.4 Limitations
In order to make the perfect collateral optimization model for a specific financial institution, one would need to get an accurate inventory of the collateral positions. However, in this thesis the work and cost for this isn’t considered in the implementation due to lack of reference data. Another limitation of this thesis is that even though some data is gathered as reference, the thesis doesn’t handle any type of real life example. This makes it hard to fully investigate how the exactness of the collateral inventory and the costs that follows affects the collateral optimization model, which is the reason for only composing this and not fully implementing it into the collateral optimization model.
1.5 Disposition
This thesis starts with this chapter called Introduction followed by the four chapters Theory, Method, Results and Discussion. The chapter Theory contains the relevant theory to create a collateral opti- mization model starting by the fundamental facts (the quality of different collateral types, the collateral markets, legal agreements and regulatory institutions and documents). This is followed by some theory specific for this thesis called collateral management. Here, central clearing is presented followed by collateral requirements, costs and some tools to manage the risk of a collateral portfolio. After this, the collateral optimization problem is described as an issue with two parts: collateral valuation and the collateral allocation to cover the risk of trading by a clearinghouse. The Theory chapter ends by presenting the most common techniques to solve a linear optimization problem. After this comes the chapter called Method that contains the method to optimize the collateral usage, the input data to the collateral optimization model as well as the implementation approach and the output that comes with it. The results of this thesis is gathered in chapter 4, which later are discussed in chapter 5 where suggestions of future work also are presented.
Theory
This chapter starts by specifying different types of collateral and its properties. With this established, the collateral market and regulations are defined, which is done to describe the components and usage of collaterals. It is also evaluated to identify the means that can be used to transform collateral and to investigate the settlement procedures in order to identify possible costs. After this, a dealer bank’s collateral management and relation with the collateral market is illustrated together with the connection to centralized clearing where risks, costs and collateral requirements also are presented. The chapter continues with describing the risks and costs of acquiring, transforming and using collateral in order to produce a legitimate cost model. By this, the optimization of the cost model and optimization of allocation to clearinghouses are presented along with the operational research.
2.1 Collateral
Collateral can be described as an easily priced liquid asset used in an agreement to provide cover against credit risk exposure, and serves to diminish loss in case of a counterpartys’ default. A liquid asset is defined as cash or something that quickly can be converted into cash with minimum affect on the market price, e.g. government bonds, corporate bonds, bills, equities, metals commodities, etc. Depending on how usable a specific collateral is to a collateral taker, it can either be labeled acceptable or unacceptable. If a clearinghouse labels the collateral as acceptable, it means that i accepts the collateral to be used. The acceptable collaterals are further divided into High Quality Liquid Assets (HQLA) and High Quality Assets (HQA). To determine if a specific collateral is a HQLA, one need to consider the Level 1 and Level 2 definitions of the Basel III regulations regarding Liquidity Coverage Ratio [2]. HQA on the other hand has a wider definition where the collateral takers normally decides which collateral types that belongs here by considering the usability of these. Some examples of collateral holders are central counterparties, central banks, banking institutions, Central Securities Depositories (CSDs) etc. The collateral market is further described in Section 2.1.2 below.
2.1.1 Credit quality rating
A way to compare and evaluate the credit risk of a specific business or government is to use credit ratings. These ratings can further be used to distinguish the quality of different collaterals.
Sovereign credit ratings are used to compare different government bonds, where the credit risk level is used to investigate the level of risk of the investing environment of a country. To compare the credit
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quality of the financial instruments of a corporation, such as corporate bonds or stocks, one can look at credit ratings from different credit rating agencies (Standard&Poor’s, Moodys and Fitch Ratings).
These rating agencies use letter designations such as A, B and C where A is highest and C lowest.
Higher grades implies that the probability of default is lower, and the lower grades implies a somewhat higher default risk.
2.1.2 Collateral markets
The collateral markets are here described to originate from a dealer bank’s perspective. As earlier mentioned, collateral is used by financial market participants to protect themselves against credit exposures and are especially used for repurchase agreements, secured lending, derivatives transactions and by the central bank market. The usage in these markets are further described in the subsections below.
2.1.2.1 Repurchasing agreement (Repo)
A repurchasing agreement, repo, is a loan secured against collateral where the transaction involves one party selling assets to a counterparty and at the same time commits to repurchase the same or similar assets from the counterparty at maturity. [3] In this case the assets can be defined as securities or other securities collateral, where the payment can be in cash or a cash equivalent collateral. This is further illustrated in Figure 2.1. Due to the fact that the value of a sold security and any securities collateral will change on a daily basis, repo transactions are subject to mark-to-market. This means that one needs to account of daily accruals on both the securities and the cash.
Between the sale and the repurchase, the seller gets use of the cash and the buyer gets legal title to the securities and can re-use them during the term of the repo by selling the assets outright, repo-ing them or pledging them to a third party. However, the buyer needs to buy back the assets before the end of the original repo in order to be able to sell them back to the seller. If the seller defaults, the buyer can liquidate the securities to repay some or all of the cash. [4]
Buyer Seller
1a. collateral securities 1b. cash
2b. return on cash
2a. returned collateral securities 2b. returned cash
Figure 2.1 – Repurchase agreement. At (1a), the Seller sells assets to the Buyer that (1b) uses cash or cash equivalent to mitigate the seller’s risk of not being able to return its assets. At maturity, the Seller (2a) repurchase the assets sold and to account for an eventual change in the securities value, the seller pays the mark-to-market price, (2b).
2.1.2.2 Securities Lending
The collateral in securities lending and borrowing is used to mitigate the lender’s risk of not being able to return borrowed securities. In the same way, the borrowed securities act as protection against the case where the lender fails to return the collateral, which is typically in the form of cash or other securities. This is further shown in Figure 2.2. Securities lending and borrowing operates the same way as repo agreements when securities lending is against cash with the difference that different legal agreements apply and the securities lent here are often equities. [4]
Securities Lender Security
Borrower
1a. collateral securities 1b. cash or collateral
Fee
2a. returned collateral securities 2b. returned cash or collateral
Figure 2.2 – Securities Lending. At (1a), the Lender lends securities to the Borrower that (1b) uses cash or cash equivalent to mitigate the lenders’s risk of not being able to return its securities. At maturity, the Lender (2a) repurchase the securities sold and to account for an eventual change in the securities value, pays the mark-to-market price, (2b).
As can be seen in Figure 2.2, the borrower pays a fee to the lender for the use of the loaned security.
The securities lending market is especially popular to use when dealing with less attractive collaterals that one wants to transform into more liquid securities.
2.1.2.3 The derivatives market
A derivative is a contract between a buyer and a seller concerning a transaction to be completed in a future point of time. The main types of derivatives are forwards, futures, options and swaps where the main categories of underlying assets are interest rates, foreign exchange, equity and commodities. In the derivatives market, fully standardized products are traded on exchanges, while more idiosyncratic products are traded bilaterally over the counter (OTC), which means that most derivatives are on the OTC market.
To describe the derivatives market one can say that it works as a large professional wholesale market, called inter-dealer market, where trading occurs between large broker-dealers such as banks, invest- ment firms or securities houses.
Due to the fact that the OTC derivatives market have non-consistent infrastructure services, several third-party service providers are available at all the steps. Exchange-traded derivatives are cleared by central counterparties, where OTC derivatives can be cleared on both bilateral basis and through central counterparties. [5] However, due to the fact that the derivatives market has grown, the impor- tance of counterparty risk has grown with it and the regulatory connected to the OTC market most of the time demands centrally cleared derivatives.
2.1.2.3.1 Exchange-traded derivatives
Exchange-traded derivatives (ETD) are derivatives traded through derivatives exchanges. A derivatives exchange can be described as a market where the parties trade standardized contracts that are pre- defined by the exchange. This means that the derivatives exchange acts as an intermediary to all related transactions, and takes initial margin from both parties as a guarantee.
Exchange Traded (Standardized) = Market Risk 2.1.2.3.2 Over-the-counter derivatives
The OTC derivative market is the largest market for derivatives and mainly involves parties such as banks or hedge funds. Comparing the bilateral and centrally cleared OTC derivatives markets (similar to ETD market), the participants in bilateral markets are more exposed to the default risk and capital charges. In bilateral markets the costs arise from counterparty risk, funding and capital, where the costs in the central clearing market mainly is the funding cost with smaller capital charges. [6]
Bilateral OTC Traded (Customized) = Market Risk + Counterparty Risk
The market for selling and purchasing currencies can be described as an OTC-market where there is no organized exchange on which currencies are traded. The most common participants here is the commercial banks who provide two-way quotes for a number of currencies. This means that each bank will quote a bid/ask rate for buying/selling a specific currency. The difference between these is called spread and can be called the source of profit for the dealer. Considering the foreign-exchange market, one always use the words buy, sell, purchase and sale from the perspective of a dealer. This means that if a dealer buys a foreign currency, the payment is equivalent in terms of the domestic currency, and if the dealer sells a foreign currency, the equivalent amount in terms of the domestic currency will be taken. [7][6]
2.1.3 Legal agreement
There are several different legal agreements that applies to the collateral markets and due to its complexity and comprehensive documentation, gathered in Table 2.1 to be further investigated when charting the collaterals in a dealer bank’s collateral portfolio.
Table 2.1 – The legal agreements required to use the different collateral markets.
Collateral market Legal agreement
Repurchase Agreement (Repo)
Global Master Repurchase Agreement
(GMRA) Securities Lending
Global Master Securities Lending Agreement (GMSLA) OTC-Derivatives
(cleared) and Exchange Traded Derivatives (ETD)
Product specific operational legal agreement for
clearing with central counterparties and exchange specific documents OTC-Derivatives
(uncleared)
International Swaps and Derivatives Association (ISDA)
Credit Support Annex (CSA) to the Master Service Agreement (MSA)
2.1.4 Regulation
The financial crisis in 2008 resulted in stricter regulations which is very much applied on the usage of collaterals. Examples of this are mandatory clearing of standardized derivatives and higher capital requirements for transactions without clearing requirements. These regulations applies on every part of the collateral market and are globally coordinated by Financial Stability Board (FSB) and Basel Committee on Banking Supervision (BCBS). A short description of these rules and regulation can be seen below. [6][8]
Liquid Coverage Ratio (LCR) and Net Stable Funding Ratio (NSFR) are developed to achieve separate, but complementary objectives and are a part of BCBS package of reform measures (Basel III). LCR helps a bank to ensure that it has a sufficient amount of HQLA to survive a stress scenario lasting for a month forward. The NSFR however, helps the bank to maintain a stable funding profile with the help of longer-term funding strategies. [8]
Shadow banking rules. To minimize risk for the shadow banking sector (the collection of non-bank financial intermediaries), the FSB have decided to apply mandatory haircuts1 for securities that isn’t cleared by central clearing, e.g. repo transactions and securities lending. [8]
1Further described in Section 2.2.2.2
The European Market Infrastructure Regulation (EMIR) is a part of Europe’s actions to in- crease the transparancy in the OTC derivatives market and reduce counterparty risk. EMIR requires that liquid swaps (liquid derivative contracts) should be cleared at a central counterpart such as a clearinghouse, meaning that both the sell and buy side needs to post initial margin (IM) and variation margin (VM). The IM and VM can typically be in the form of HQLA (cash, AAA-rated government bonds). [8]
The second Markets in Finacial Instruments Directive (MiFID II) requires that all trading of derivatives that are adequately liquid and suitable for clearing take place on regulated trading venues such as organised trading facilities (OTFs), regulated markets or multilateral trading facilities (MTFs). In the US, the Dodd-Frank Act establish all these new measures and structures.
The Basel Committe on Banking Supervision/International Organisation of Securities Com- missions (BCBS-IOSCO) framework establish further steps to be taken between parties which handles with non-centrally cleared OTC-derivative instruments. Some examples of steps that are either seen as optional or not performed at this moment are calculation of exposure and resulting exchange of VM, exchange of two-way IM (requiring amendments within the ISDA CSA) and establishment of policies for minimize disputes by reconciling portfolios, risk sensitivities, risk factors and margin calls with counterparties. [8]
The applied regulation of the different markets are summarized in Table 2.2. [9]
Table 2.2 – Regulations that should be taken into consideration for Collateral management.
Collateral market Regulation Repurchase Agreement
(Repo)
FSB framework to standardize
repo haircuts Securities Lending
FSB framework on shadow banking
requirements OTC-Derivatives
(cleared) and Exchange Traded Derivatives (ETD)
EMIR or Dodd-Frank
Act in the US OTC-Derivatives
(uncleared) BCBS-IOSCO
2.2 Collateral management
Collateral management is a key function with close links to trading, treasury risk, liquidity manage- ment and capital optimization.[10] The easiest form of collateral management is that the financial institution have several separate desks that each have a collateral portfolio to use. But in order to optimize the collateral usage in a bank, one should centralize the management of this collateral, mean- ing that instead of having several different desk that each handle collateral there can be a central one, see Figure 2.3. The pros of having it this way is that if one desk lacks of a certain collateral, where another one have excess of this collateral, the bank doesn’t need to buy more or transform any of the other collaterals in order to cover the need in the own institution. [8]
Desk 2 Derivatives (OTC cleared/uncleared
and ETD )
Desk 3 Equities (Securities Lending)
Centralized Collateral Management Desk 1
Fixed Income (Repo)
Figure 2.3 – An illustration of centralized collateral management in a financial institution. Without centralized management, each of the three desks uses separate collateral pools for each market. By only having one collateral pool for all collateral usages, the collateral usage can be optimized.
In short, with centralized management, the bank can select and trade the collaterals across all products and trading. Also, all requirements are centralized monitored which simplifies the funding, making it firm-wide. Since all collaterals are gathered in the same pool, this can be handled as one large port- folio of collaterals. To optimize the collateral usage, there needs to be a comprehensive investigation over all collaterals available in the institution. The inventory needs to cover both existing collateral and collateral kept in other institutions such as custodians and central securities depositories (CSDs), together with an overview of the assets that can be converted into eligible collateral by securitisation.
In short, all collateral positions in the bank needs to be monitored.[8]
After this, the bank needs to keep this collateral pool to be as liquid as the regulatory institutions demands, and also follow other rules and guidelines regarding these collaterals. The collateral pool composition and size should further be allocated to optimally match the needs, and effectively allocate to cover risk margin values set by the counterparties. [11]
2.2.1 Collateral transformation
Due to recent regulations it will be mandatory to use a CCP for standard OTC-derivatives, which implies an increased demand for high-quality collateral assets. From the regulations regarding the Liquidity Coverage Ratio (LCR), every financial institution should hold a buffer of HQLA on their balance sheets as well as other assets that can be used as collateral. In the case where a financial institution doesn’t hold the desired quality or types of collateral that a clearinghouse demands, the problem can be solved by collateral transformation. [1]
Collateral transformation (also called collateral upgrades or collateral swaps) are services where a dealer bank can be offered to upgrade lower quality assets into CCP eligible collateral. Collateral transformation can also be used to adjust the portfolio of collaterals to use the portfolio in the most efficient and least costly way. In order to transform collateral, a financial institution can e.g. trade on the repo or securities lending market or use an external services provider (securities settlement systems, payment systems, internal systems of custodians etc.), see Table 2.3 below. [5] To further illustrate the collateral market and its connection to the dealer bank, see Figure 2.4.
Table 2.3 – The collateral usage in the market from a dealer bank’s perspective.
Collateral market Description Repurchase Agreement
(Repo)
To secure cash replacements,
collateral in form of bonds or equity are used
Securities Lending
To secure a loaned security, cash or other collateral
is delivered OTC-Derivatives
(cleared) and Exchange Traded Derivatives (ETD)
Collateral is delivered to or from a CCP to cover risk margin value.
Includes initial margin (IM) and variation margin (VM)
OTC-Derivatives (uncleared)
Collateral is moved between trading
counterparties.
Mainly variation margin (VM)
Repo transactions and securities lending are earlier discussed, and since the actions taken by hedge funds and central banks reminds of these, it is only described briefly. Here a prime brokerage is de- scribed as a special group of services that many brokerages give to special clients. The services provided under prime brokering include securities lending, leveraged trade executions and cash management, among other things. The main function of a central bank is to control the nation’s money supply. Most central banks undertake repo transactions in the market to control short-term interest. The dealer bank can also trade uncleared OTC-derivatives, however this is not depicted in Figure 2.4 due to the fact that only the collateral transformation and central clearing are of interest here.
Central Banks
DEALER BANK with
Centralized Collateral Management
Custodians Money Market
Funds
CCPs
Hedge Funds Collateral Cash
Collateral Cash
SHORT-TERM (REPO) FUNDING
Collateral Cash/Collateral
SECURITIES LENDING
RISK TRANSFER OTC + Exchange
derivatives
Cash/Collateral
Col lateral Cash
PRIM E
BROKERA GE
Figure 2.4 – This is the usages of collateral for a dealer bank. The bank uses central counterparties (CCPs) to transfer the risk with OTC derivatives or ETD, and by this, the bank needs to pledge collateral to cover the risk margin value of these contracts. In order to transform collateral to cash or the other way around the bank can use different financial organizations to borrow (transform) the collateral/cash.
With the transformation comes also a fee the dealer bank needs to pay. [12]
2.2.2 Centralized clearing
Clearing through clearinghouses acting as CCP’s are created to manage and reduce counterparty risk in bilateral markets, illustrated in Figure 2.5.
The legal process of replacing the original counterparties and becoming the single counterparty for all participants is generally called novation. Novation gives the clearinghouse a huge portfolio that always are balanced and not affected by market risk due to its offsetting positions, but the clearinghouse do experience a huge counterparty risk, and faces the earlier mention risk; that one of the parties will fall into default. The CCPs main function is to be between counterparties acting as the buyer to every seller, and seller to every buyer, accepting all obligations and rights that comes with it. By this the counterparty and systemic risks will be reduced and the CCPs reallocate the default losses through different methods such as demanding collateral (margin) requirements from their clearing members.
P1 P3
P4 P2
P1 CCP P3
P4 P2
31
7 5
8
3
12 3
4 7
Figure 2.5 – The illustration to the left describes an example of bilateral netting where the figure to the right illustrates centrally cleared markets. P 1, P 2, P 3 and P 4 can here be described as counterparties in the left illustration and direct clearing members to a clearinghouse in the right illustration.
The general role of a CCP is to take responsibility for closing out all the positions of a defaulting clearing member, but also to set rules and standards for the clearing members. In order to cover the losses in the case of a clearing member defaulting, the clearinghouse maintains a default fund and other financial resources required from the clearing members in form of initial margin and variation margin.
The initial margin is to cover the worst case liquidation or close-out costs where the variation margin trails the market movement. [6]
2.2.2.1 Risks of Central Clearing
The derivatives that are centrally cleared can only be liquid, standardized, non-exotic products. With a derivatives contract comes several risks such as market risk, credit risk, operational risk, legal risk, liquidity risk, counterparty risk and integration of risk types. However, in central clearing the clearing member isn’t as exposed as in bilateral clearing since the CCP takes responsibility for the risks and asks for collateral to cover these. Even if a clearinghouse offers advantages such as risk reduction and operational efficiencies, they also demands significant collateralisation, centralization of counterparty risk and loss-mutualisation. Also, if the clearinghouse would default or fail the impact would appear as a systematic disturbance, meaning that the whole market would get affected. By this, the clearinghouses creates arising operational, liquidity and systematic risks. [6]
2.2.2.2 Requirements and constraints
Considering that the exposure of a clearinghouse is very high, one can think that a clearinghouse should demand a lot of collateral. But on the other hand, if the clearinghouse demands too much, the clearing members will take their business elsewhere. Since this is a pretty delicate balance board, the clearinghouses need a great approach of calculating the risk of the contracts it clears. The most crucial when deciding the collateral deposit of a contract is that the clearinghouse needs to understand the risks, i.e. decide which risks are acceptable, manage these and avoid the unacceptable risks.
There are several ways to calculate the risk where the most used ones are Value at Risk (VaR), standardized portfolio analysis of risk (SPAN) and Expected Shortfall (ES), where the clearinghouses always have their own twist on these. The risk algorithm comes up with a risk margin value per portfolio, also called margin requirement or initial margin, where the collateral should be valued at at least this amount after haircuts. Mutual for these risk calculations, one can say that the expected value of collateral should be equal to the expected loss given the case of default.[5]
Expected loss given default = Expected value of collateral
As earlier mentioned, clearinghouses have different requirements on different types of collaterals, in the subsections below are the most general requirements gathered and furthered described.
2.2.2.2.1 Initial margin and Variation margin
The clearinghouses usually demands Initial Margin (IM) and Variation Margin (VM) to protect them- selves from the fluctuations of market movements in case of a clearing members default. Securities and cash collaterals can be used to meet these margin calls, though securities collateral may be subject to haircuts from CCPs. If a clearinghouse were to demand collaterals above the actual risk value, the collaterals will be returned at the end of the transaction.
2.2.2.2.2 Haircut
When collaterals are being pledged to a clearinghouse, the collateral suffer from a reduced valuation by some percentage called haircut. The percentage the collateral being reduced to is determined by the amount of risk associated by the lender. If the collateral are cash and in domestic currency, the clearinghouses normally always accept and don’t apply a haircut, however if its in a foreign currency the haircut normally is high and it is more seldom accepted as collateral. Government bonds is often accepted as collateral and the haircut is low, where corporate bonds have a higher haircut and is seldom accepted. The haircut for a bank guarantee collateral is low, or even none, but only sometimes accepted by the clearinghouses.
Haircuts exist to allow collaterals to have price variability. Theoretically, the haircut is driven by the volatility and liquidity of the specific collateral but in practice the haircut levels are predetermined by the clearinghouses and don’t change as the market changes. Haircut are primarily created to account for market risk stemming from the price volatility. When deciding upon a haircut, the clearinghouses consider the default risk, maturity and liquidity of the collateral security. It also considers the time taken to liquidate the collateral, the volatility of the underlying market variables defining the value
of the collateral and wrong-way risk, meaning the relationship between the value of collateral and the exposure or default of the counterparty.
Example: Haircut
Considering a contract going through CCP, where the calculated risk margin value is $10 000.
The clearing member will cover the risk margin value using a collateral security with a haircut of 95%. This means that the clearing member needs to use collateral worth $10 526.36 to cover the risk margin value.
Collateral with market value · Haircut = Risk value Collateral with market value = Risk value
Haircut =$10 000
0.95 ∼ $10 526.36
2.2.2.2.3 Credit quality
The credit quality influence the importance of the collaterals due to its relation with haircuts, e.g.
for a high rating, the haircut becomes lower than for a collateral with lower rating. This also applies to the clearing members explicit, if a clearing member has a high rating, the initial margin becomes somewhat lower than for a clearing member with a lower credit rating.
2.2.2.2.4 Lower and upper concentration limits
Besides the properties mentioned above, clearinghouses can also have upper and lower concentration limits on certain collaterals. The lower limits usually can be due to their preferences, certain collaterals is simply considered more valuable and usable than others. The upper limits is mainly due to the opposite, that a certain clearinghouse doesn’t prefer a certain collateral. The lower and upper limit can also depend on this preference system with the combination of the risk margin value, if the risk margin value is relatively large and the clearinghouse feels strongly about a certain collateral, this collateral might get a higher or lower limit.
2.2.2.3 Central counterparty charges
In short, the main costs for a dealer bank when using a CCP is the funding and lower capital costs, but to clarify the cost components connected to central clearing it is summarized below:[13]
• Inital Margin (IM) and Variation Margin (VM): Described earlier, mainly in cash and securities collaterals.
• Clearing fees: Paid in cash with usually a volume-based transaction, but can also be monthly payments.
• Settlement charges: CPPs acquire settlement charges from clearing members on transactions going through the clearinghouse.
• Default fund contribution: All clearing members needs to contribute to the clearinghouse’s default fund.
• Other charges: Such as service provider charges and the cost to have operations staffs, involved to support central clearing. Technology used in the banks can also be large portion of the operating cost.
Besides the costs directly related to the clearinghouse, there are several other costs that needs to taken into consideration to fully manage the collateral usages. A hidden charge with central clearing is that most CCPs demands that its clearing members needs to set up bank accounts at approved settlement banks to secure payments. These banks can charge the clearing members for different services such as wire transfers, reports, account access etc. However, if the clearing member actually is a bank, the these costs can be ignored.
Other indirect charges can be in case of transferring securities collateral, the clearing members can be charged settlement charges that arises from the fact that a CCP needs to go through a Central Securities Depository (CSD).
2.2.3 Collateral cost model
When the collateral inventory and transformation actions are defined one can continue by identifying the costs regarding the collaterals. In order to model the cost in a comprehensive manner, it is recom- mended trying to truly understand the specific cost structure of the bank, and translate this into cost per trade and by this also identifying the costs of collaterals.
However, to optimize the use of collaterals, one could also consider the total costs involved when using different assets as collateral. Even though most costs are rather explicit, it can be difficult to fully survey all in a satisfying way. Costs that are relatively easy to study is for example the cost of acquiring collateral and transferring different collaterals to a counterparty. Costs that can be harder to be protected from are costs such as opportunity cost.
There are different costs for different financial instruments, and in this section we’re going to try to scrutinize the most general costs where the prior to this is to minimize the collateral cost.
To measure the costs and value the different collaterals in a consistent way, Basis Points (BPS) are used.
Basis Points (BPS)
BPS is a common unit of measure for interest rates and other percentages in finance where one basis point refers to 1001 th of 1%, i.e. 0.01%. This means that a change of 1% can be translated as 100 basis points. Basis point is mainly used in order to minimize the confusion. For example, if a rate of 10% that has an increase of 10% it can sometimes be hard to interpret this correctly and its better to say that the rate has an increase of 1000 basis points, i.e 10%·(1 + 0.1) = 11%.[14]
2.2.3.1 Funding costs
Funding costs can either be the price tag of a specific collateral, or by looking at the active contracts the funding value adjustment can be calculated together with the collateral value adjustment to know how much this transfer is expected to cost.
Earlier, banks and other financial institutions weren’t handling funding costs when dealing with deriva- tive contracts. This was however changed after the Lehman Brothers bankruptcy in 2008, where the wholesale markets were drained, creating a huge funding problem for banks and forcing them to rely on central bank liquidity. Now, the factors that regulate the funding costs are the clearing mandate,
bilateral collateral rules, liquidity coverage ratio, net stable funding ratio, increased capital require- ments and leverage ratio. This have led banks to be more aware of the need to manage the funding costs, which have created the concept of funding value adjustment (FVA) and margin value adjustment (MVA). FVA is associated with the funding of derivatives, where MVA concerns the need to post the initial margin.
Funding costs is asset-specific and an example of costs concerning a high quality treasury bond is haircut and spread due to the fact that this bond can easily be used on the repomarket in order to transform its value into cash. Here, the cost of borrowing money on an unsecured basis to buy the bond isn’t considered. Derivatives assets (such as stocks bonds, commodities, currencies, interest rates and market indexes) can be used as collateral, but can not be repoed. For assessing the underlying funding costs for derivatives, the bank fund itself through many different sources. There is no right way in doing this, but typically the banks treasury department will generate a blended cost of funds curve that consist of all major currencies, this is also called funds transfer pricing curve (FTP curve). [6]
A difficulty with funding costs is that it can be hard to track down every cost that affect the final funding cost of a collateral. However, there also exists costs that may be obvious, such as initial and variation margin. Due to the fact that variation margin is posted against a Mark-to-Market (MTM) loss, one cannot consider this an explicit funding cost. Initial margin on the other hand is not posted against MTM losses, and by this it is a funding cost, which is another good reason for splitting funding costs into MVA and FVA. [6] The variety of funding costs is also affected by the type of collateral. This is due to the fact that if posting non-cash collateral, the haircut may be lower and by this, one doesn’t need as much funding for this collateral. Also, the return paid on the collateral is of interest since variation margin in a Credit Support Annex (CSA) generally is remunerated at the overnight indexed swap (OIS) in the relevant currency, which is often viewed as a reasonable proxy for the risk-free-rate.
In this case, the funding cost is the cost above the risk free rate, and if collateral is less than OIS then the funding cost should be higher.
Shortly, the funding costs represents the cost of use for a collateral asset. In order to apply funding costs to individual positions, a common approach is to group them into different categories based on credit quality, internal availability or ownership, eligibility at central funding venues and maturity.
An acceptable way to measure the credit quality is to use some well-established credit rating system, such as the credit rating agencies Standard & Poors’, Moody’s or Fitch Ratings. Another parameter connected to the funding costs could be the region in which the assets is mostly connected to. This is interesting due to the risks connected to systematic risk and other risk such as wrong way risk also may affect.
2.2.3.2 Additional costs
When selecting appropriate collateral one needs to consider the liquidity, volatility, avoiding strong correlation with exposure, avoiding positive correlation to collateral giver and keep the collateral portfolio well diversified. These cost factors are considered additional costs and are costs to the counterparty such as the moving, settling and/or safekeeping of the collateral assets. In the subsections below are a description of TCA, custodial fees, and safekeeping fees.
2.2.3.2.1 Transaction cost analysis
Transaction cost analysis (TCA) exists in order to help traders, investment managers and firms to better understand how well they traded and how it can be improved.
Investment related transaction costs is the costs the comes from a time delay between the investment decision and the order being released to the market. The longer it takes for the manager and trader to resolve these issues, the risk of an adverse price movement arises, and with it, the cost.
The largest subset of transaction costs is the transaction cost related to trading, which includes the costs that occur during the time period from the start, to the end of the trading. [15] Since these costs cannot be eliminated, they need to be managed in a satisfying way, and the first step in doing so is to analyze the components in question. The components that have the largest effect of the trading related transaction costs are market impact and timing risk. [16]
If the order aren’t fully executed within the allotted period of time, the forgone profit or loss is represented by the opportunity cost, which can be measured by the number of unexecuted shares multiplied by the price change during which the order was in the market. [16]
To summarize, there are three classifications of transaction costs; Investment- , trading- and opportu- nity costs, and every classification have some cost components that belongs to, which can be seen in Figure 2.6.
Trading Costs Commission
Fees Rebates Spreads Price Appreciation
Market Impact Timing Risk
Opportunity Cost Opportunity Cost Transaction Costs
Investment Costs Taxes Delay Cost
Figure 2.6 – Transaction costs classification. [16]
In order to categorize these costs further, it’s stated that there are some general properties that these costs can possess such as fixed, variable, visible and hidden. The fixed cost are those that don’t depend on the investment strategy which means that they cannot be changed. Variable costs on the other hand are the costs where money managers, traders and brokers control the variable components in the investment process to be consistent with the overall investment objective of the fund by adding a substantial value.
The visible costs, also called transparent or explicit, are those that can be analyzed in advance. An example of a visible cost can be a percentage of something such as $USD/share. The hidden, also called non-transparent or implicit, are those costs whose fee structure is unknown. These costs usually are estimated using statistical models. A summary of which properties the components possess can be seen in Figure 2.4.
Table 2.4 – Unbundled transaction costs. [16]
Fixed Variable
Visible
Commission Spreads
Fees Taxes
Rebates
Hidden
Delay Cost Price Appreciation
Market Impact Timing Risk Opportunity
In order to learn more about the transaction cost components, see [17]. The transaction cost compo- nents that can be identified are the following:
Commission is the payment made to broker-dealers for executing trades. Normally expressed on a per share basis or based on total transaction value. The payment is normally a fixed, explicit cost.
Fees, also called exchange fees, are also an explicit cost (”visible”) and is charged when the order is executed. This cost includes the clearing and settlement costs, the securities exchange transaction fees, as well as the ticket charges assessed by floor brokers.
Taxes are considered as a visible, explicit investment related cost and varies by type of earning.
Rebates is a fairly new transaction cost. [16] An example of this is that if an investor posts liquidity, the investor is provided with a rebate where the party receiving the liquidity is charged a fee.
The fee should always be larger than the rebate in order to ensure that the trading venue will earn a profit.
Spreads is an explicit cost connected to the trading costs. The definition of a spread is the difference between the best ask and best bid price, and it is used to compensate market makers for the risks of holding and acquiring an inventory while waiting to offset the position in the market.
Delay cost is the cost in investment value that comes from a time delay between the manager making the investment decision and the time the order is released to the market.
Price Appreciation, also called price trend, drift, momentum or alpha, and can be described as a
”natural price movement” that demonstrates how the price would evolve in the market without uncertainty.
Market Impact is the movement in the price of a equity caused by a specific trade. This is one of the more influential in the transaction cost components and can mathematically be described as the difference between the price trajectory of the equity with the order and what the price trajectory would have been if the order had not been released into the market. Due to the fact that none of these factors can be measured with satisfying precision, the market impact have been called the ”Heisenberg uncertainty principle of trading”.
Timing Risk consists of three components; price volatility, liquidity risk and parameter estimation error. All components suffers from the risk that the estimated transaction cost wont be adequate with the real ones. Price volatility causes the underlying equity to be either higher or lower than the estimated one. The liquidity risk drives the market impact cost due to fluctuations in the number of counterparties in the market and depends of volumes, intra-day trading patterns and the buying and selling pressure of all market participants. The estimation error is here the uncertainty surrounding the market impact parameters.
Opportunity Cost is used to measure the avoided loss or forgone profit of not being able to transact the entire order. The main reasons of rising opportunity costs is due to adverse price movements and insufficient liquidity.
2.2.3.2.2 Custodial Fees and Safekeeping Fees
The custodian fee is the fee charged by a broker or financial institution in order to be able to offer safekeeping services. This means that the broker or financial institution holds securities or assets safe, collects the dividend and interest income and gives a monthly or quarterly account statement for the owner. Safekeeping Fees are applied when a brokerage holds a client’s securities or other assets on the clients behalf.
2.2.4 Risk management
The word risk is most commonly associated with the risk of loosing money and have been mentioned earlier in the thesis, but to summarize; The main types of risks connected to collateral management are: credit risk, market risk, operational risk and liquidity risk.
Credit risk, also called default risk, is the risk that one party in a financial agreement will fail to meet its obligations. One can divide credit risk into credit default risk, concentration risk and country risk.
All these risks of a contract can, as earlier mentioned, be reduced by a central counterparty. However, in order to calculate the total risk of a specific collateral, the credit risk is of interest. There are several different approaches to measure and manage risk, such as exposure at default (EAD), expected loss (EL), loss given default (LGD), probability of default (PD) and Value at risk (VaR).
Market risk is the risk of losses due to change in the valuation of a financial asset. By modeling the volatility and measuring this with with VaR, the market risk of a collateral can be determined.
Operational risk is the risk of losing money if the process of handling financial assets are inadequate.
This risk is harder to model and interpret than the earlier mentioned one, but can be a huge factor
when dealing with collaterals.
Liquidity risk is the risk of a financial asset not being able to be traded fast enough to prevent a loss.
There are two types of liquidity risk, asset and funding liquidity. To measure this risk, one can use liquidity-adjusted value at risk, which is further described in Section 2.2.4.3. [18]
The main purpose of a risk measure is to determine how much of a financial asset is needed to make the risks taken by financial institutions acceptable and accordance with the regulations.
2.2.4.1 Volatility
Volatility, σ, is the variation of the return of a security and is derived from the market price over time.
Here, either the volatility of a specific collateral can be determined, or the volatility of the market where the collateral belongs.
In order to measure the stock and bond market volatilities, the theory from the thesis ”Sovereign credit ratings market volatility and financial gains”, [19], are used. For every region i at time t, the stock market return rstocki,t are defined as
rstocki,t = ln(stocki,t) − ln(stocki,t−1), (2.1)
which is the difference in logarithmic price at time t and t − 1. Equation 2.1 also holds for other assets, such as currencies and commodities. However, the bond market return rbondi,t is defined as the difference in logarithmic yield at time t and t − 1,
rbondi,t = ln(yieldi,t) − ln(yieldi,t−1).
Using these returns, a volatility model can be applied in order to simulate the volatility in the market.
Observe that the same described approach can be used to get the volatility of a specific collateral by ignoring the region, i.
2.2.4.1.1 GARCH(1,1)
The generalized autoregressive conditional heteroskedasticity (GARCH) model is a univariate volatility model where the volatility can be modeled by
σt2= ω +
q
X
j=1
αjYt−j2 +
p
X
j=1
βjσt−j2
and ω, α and β are estimated parameters that needs to be positive to ensure positive volatility forecasts, α, ω, β > 0. Also, α + β < 1 to ensure covariance stationarity. [20]
The most common version of GARCH is with one lag, GARCH(1,1),
σ2t = ω + αYt−12 + βσt−12 .
2.2.4.1.2 EGARCH(1,1)
There are several different forms of the GARCH model, and one of these is exponential generalized autoregressive conditional heteroskedasticity (EGARCH) which was introduced by Nelson and Cao (1991).[19] With one lag, the model can be written as
log(σi,t2 ) = ωi+ αi(zi,t−1) + βilog(σ2i,t−1) + δi(|zi,t−1| − E(|zi,t−1|)),
where the parameter δi is estimated along with αi and βi, and i in this case is related to the earlier mentioned regions. Here, the E(zi,t−) is the expected value of the standardized residuals.[19]
2.2.4.2 Value at Risk
Value at Risk, VaR, is a measure of market risk and measure the worst expected loss that a firm can suffer during a period of time and normal market conditions at a specified confidence level. One can also say that VaR is a quantile of the profit/loss distribution and can be used to determine the probability of loosing a certain amount of cash given a period of time. A common way to write this risk measure is V aRα·100%(L) where L is the sorted losses and α ∈ (0, 1) is to the probability level, usually set to 0.99 to be compliant with regulatory demands.
One way of calculating the V aR of an asset is to use historical observations and a statistical model to estimate the probability distribution. From the historical observations, possible future scenarios can be generated, and from this the profit and loss vector are created at a specific time t,
P nLi= V − Vi, (2.2)
where V is the value of the asset and i corresponds to the scenario i and i = 1, .., N . This vector is sorted in decreasing order where the α · N :th element the worst expected loss,
V aRα·100%(L) = P nL(α · N ). (2.3)
However, this value, V aRα100%(L), does not capture risk exposures such as operational risk, liquidity risk, regulatory risk or sovereign risk. [21]
To determine if the V aR forecast is eligible, violation ratios can be used, and is defined by V R = Observed number of violations
Expected number of violations = ν (1 − α)(WT) where ν is the number of V aR-violations in the time period WT.
2.2.4.3 Liquidity Adjusted Value at Risk
The liquidity-risk adjusted value at risk, LAdj − V aR, can be calculated by assuming that the liquidity risk can be described by a bid-ask spread and added on the conventional VaR measure.[22] Assume that the bid-ask spread is stochastic and the relative spread, S can be used for modeling,
S =bid-ask spread mid-price .
The average relative spread, S, plus a multiple of the volatility, σ, of the relative spread to cover most, say 99%, of the spread distribution, gives the liquidity-risk adjusted VaR,
LAdj-VaR = V aR +1
2Mid · (S + aσ),
where Mid is the mid-price and a is a scaling factor such that one achieve 99% probability coverage of the change in the relative spread.[22]
2.2.4.4 Probability of default
Probability of default (PD) is defined as the likelihood that a counterparty can’t repay its debts and fall into default. To calculate PD, one need to take the credit history into consideration. PD take values between 0-100% where a higher percentage implies more risk than a low percentage. There are many appraoches to calcuate the probability of default but if not calculated internally, PD can be gathered from rating agencies such as Standard and Poors’, Moodys and Finch.
2.2.4.5 Exposure at default
Exposure at default (EAD) can be defined as the gross exposure in the case of default of a counterparty.
The EAD parameter is mainly used in calculations regarding capital regulated by Basel for a financial institution, e.g a bank.
2.2.4.6 Loss given default
Loss given default (LGD) is a common parameter in risk models and can also be used in calculations regarding capital regulated by Basel. LGD is most commonly defined as a share of the asset that is lost in the case of a borrowers’ default.
2.2.4.7 Expected loss
As mentioned in the Section 2.2.2.2, the expected value of collateral should be equal to the expected loss (EL) given default. To calculate EL for a single asset, we can used the earlier mentioned PD, EAD and LGD
Li = P Di· EADi· LGDi, (2.4)
where i = 1, 2, ..., n and the total expected loss for a portfolio simply are calculated by adding EL for every asset.
EL =
n
X
i=1
ELi (2.5)
2.3 Collateral Optimization
The term collateral optimization includes all actions done by a financial institution in order to make a more effective use of its existing portfolio of collateral assets. One purpose of collateral optimization is to survey the use of collateral, and by this manage the risks in a more efficient way. This can in turn lead to lower funding costs, and by this, higher profits. Also, by optimizing the collateral in banks, it may boost the institution’s ability to attract extra liquidity if needed, and lower its need for costly and potentially risky collateral transformation services. [1][23]
A condition for collateral optimization is that the financial institutions, in this case a bank, have good understanding about their existing collaterals, where they need to both know the cost and use for each collateral. In order to optimize the collateral usage, the allocation of different collateral and the effective parts that the market controls can be improved. To summarize, one can say that the parameters that controls the optimization of collaterals are:
• Collateral positions
• Collateral costs
• Collateral requirements
• Settlement procedures
To specify the optimization infrastructure, the institution needs to keep track on inventory, market data, requirements and other agreement terms. If all data is gathered appropriately and the cost model can be defined in a satisfying way. [24]
2.3.1 Optimizing cost models
The collateral cost model is defined to identify all potential risks and costs with a specific collat- eral. Also, since different collateral holders have different priorities and preferences, this leads to an individual cost model for every collateral holder.
In this section, there are three different approaches ranking the collaterals internally within a dealer bank.
2.3.1.1 Preference ranking
As earlier mentioned have every institution different preferences e.g. a bank in a specific country can value this country’s currency to more than its actual market value due to its other usage areas. The easiest way to optimize the collateral usage is that the financial institutions creates its own preference ranking system. These ranking rules will of course vary, but if the institutions wishes to create a versatile ranking model it should take the following into consideration:
• credit quality
• rating
• liquidity profile
• asset class
• market segment
