Credit risk can arise in many ways, from granting loans to trading derivatives. The amount of credit risk depends largely on the structure of the agreement between the bank and its customers; for example, in a loan, the amount that the customer owes is fixed, whereas in a line of credit, the customer chooses how much to borrow each month. An agreement between a bank and a customer that creates credit exposure is often called a credit structure or a credit facility.
This chapter describes the most common credit structures. It is useful to know these structures for two reasons: to be able to have a meaningful conversation with bank credit staff, and to model the potential credit losses for each structure.
For a single facility, there are three parameters that are important in quantifying the credit risk: the exposure at default (EAD), the loss in the event of default (LIED), and the probability of default (PD). The probability of default is also known as the default rate or the expected default frequency (EDF). It is most strongly associated with the characteristics of the counterparty or customer.
The exposure at default (EAD) is also known as the loan equivalence (LEQ) and is the outstanding amount at the time of default. The loss in the event of default (LIED) is the loss as a percentage of the EAD. It is also known as loss given default (LGD) or severity (S). The amount of loss is the full EAD, plus all administrative costs associated with the default, minus the net present value of any amount that is later recovered from the defaulted company:
The EAD and LIED are strongly influenced by the type of credit structure. In discussing the alternative types of credit, we focus on how the structure affects these two loss parameters.
The credit structures discussed in this chapter are as follows:
Credit exposures to large corporations
• Commercial loans
• Commercial lines
• Letters of credit and guarantees
• Leases
• Credit derivatives
Credit exposures to retail customers
• Personal loans
• Credit cards
• Car loans
• Leases and hire-purchase agreements
• Mortgages
• Home-equity lines of credit
Credit exposures in trading operations
• Bonds
• Asset-backed securities
• Securities lending and repos
• Margin accounts
• Credit exposure for derivatives
Typically, commercial loans have a fixed structure for disbursements from the bank to the company and have a fixed schedule of repayments, including interest payments. There may also be a fee paid by the company at the initiation of the loan. The fee acts to reduce required interest payments later. The loan may be secured (collateralized) or unsecured. If it is secured, then in the event of default, the bank will take legal possession of some specified asset and be able to sell this to reduce the loss. The collateral may be in the form of traded securities, the rights to a physical inventory or building, or the rights to a stream of cash flows, such as accounts payable from customers to the corporation. An unsecured loan is a general obligation of the company, and in the case of default, the bank will just get its share of the residual value of the company. The loan may also be classified as senior or subordinated (also called junior). When a company liquidates, it pays off the senior loans first; then if there are any remaining assets, it pays off the subordinated loans. As senior loans always get paid before subordinated loans, they have a lower loss in the event of default.
For credit-risk measurement, the most important loan features are the collateral type, the level of seniority, the term (or maturity), and the scheduled amounts that are expected to be outstanding (i.e., the amount that the company owes the bank at any given time).
Very large corporate loans may be syndicated to spread the risk among several banks and reduce the concentration risk for any one bank. In the syndication process there will be one or possibly two lead banks that arrange the deal, and then get agreement from other banks to take portions of the loan. Typically, all banks share equally in the risks, in that they have equal seniority and an equal claim on collateral. Once the deal has been closed, there may be secondary trading in which banks sell the loan between each other. This is almost like bond trading except that the number of investors is limited, and much more legal paperwork needs to be completed to transfer the rights of the loan from one party to another.
The syndicated-loan market is a prime example of the way in which the loan and bond markets are converging, with loans becoming more liquid, and the business model becoming one in which bankers originate and structure the deal then sell it to external portfolio managers who are looking for investments.
In a standard loan, the pattern of disbursements and repayments is set on the day of closing the deal. For a line of credit (also known as a revolver or a commitment), only a maximum amount is set in advance. The company then draws on the line according to its needs and repays it when it wishes. This means that the bank cannot be certain about the exposure at default (EAD). Historical studies have found that companies going into default tend to draw down more than healthy companies. There are three models used for the EAD of a line of credit. The choice depends on the data available in any given situation.
EAD = A × Drawn Amount A ≥ 1
EAD = B × Line 0 ≥ B ≥ 1
EAD = Drawn Amount + C × (Line − Drawn Amount) 0 ≥ C ≥ 1
In this formulation, the Drawn Amount is the amount that the customer has currently borrowed, and the Line is the maximum amount that the customer can borrow. A, B, and C are constants that are found by looking at historical data to compare the actual exposure at default for companies that have defaulted with the Drawn Amount or the Line several months before the default happened. This is discussed later in the chapter on estimating parameter values for single facilities.
With a line of credit, the bank faces the possibility of loss on both the drawn and undrawn amounts, and should therefore set aside capital for each. However, it need only provide debt funding for the drawn amount. This is reflected in the pricing schedule, which charges the company one rate of interest for the drawn portion and another, lower, rate of interest for the additional amount that the bank has committed to lend. The charge on the drawn portion is the cost of debt plus the cost of capital. The charge on the undrawn portion is just the cost of capital.
To minimize the risk, the line agreement may also include covenants that allow the bank to limit further drawdowns if the company is downgraded. There may also be covenants so that under certain conditions, the bank can convert the line into a loan with a fixed term for repayments.
There are two primary types of letters of credit (LC): trade LCs and backup LCs. Trade LCs are tied to specific export transactions. A trade LC guarantees payment from a local importer to an overseas exporter; if the importer fails to pay, the bank will pay, and then try to reclaim the amount from the importer. For the bank, this creates a short-term exposure to the local importer.
A back-up letter of credit is a general form of guarantee or credit enhancement in which the bank agrees to make payments to a third party if the bank’s customer fails. This is used to lower the cost of the customer’s getting credit from the third party, because the third party now only faces the risk of a bank default. The bank faces the full default risk from its customer and has the same risk as if it had given the customer a direct loan. In the treatment of credit risk, such a letter of credit is considered to be a full loan, and the customer is charged by the bank for the economic capital it must set aside in case the customer defaults.
Leases are a form of collateralized loan, but with different tax treatment in certain situations. In an equipment lease, the equipment is given to the customer, and in return, the customer makes rental payments. After sufficient payments, the customer may keep the equipment. In terms of credit risk, this is equivalent to giving the customer a loan, having them buy the equipment, and pledging the equipment as collateral to secure the loan. In both cases, if the customer stops making payments, the bank ends up owning the equipment. Depending on the terms of the lease, the bank may or may not have a further claim on the company if the value of the equipment is less than the amount of the loan. The risk of leases can be treated in a very similar way to the risk of collateralized loans.
The derivatives that we discussed in the market-risk chapters have their value determined according to a market variable such as the price of an equity or the prevailing interbank lending rate. Credit derivatives are different in that they are designed so their value is primarily determined by credit events, such as a default or a downgrade. Credit derivatives have been commonly used for several years, but are still highly tailored, over-the-counter instruments. Credit derivatives are useful for several reasons:
• They allow the relatively easy transfer of credit risk without the complex legal agreements that are required to transfer the ownership of a loan.
• They allow just a part of the loan’s risk to be transferred.
• They can be tailored in many ways to transfer just one portion of the risk if desired; e.g., they could transfer the risk of default but not the risk of downgrades.
In almost all cases, the calculation of the risk for credit derivatives can be based on the analysis that would be used for the underlying loan.
As a simple example, consider a derivative in which one bank agrees to pay an initial amount, and in return, a second bank agrees to make payments equal to all the payments they receive from a particular corporate loan. For the first bank, if the corporation defaults, the bank will receive less money and will therefore make a loss. For the second bank, if the corporation defaults, the bank will receive less money from the corporation, but it will also need to pay less to the first bank. The changes in payments therefore cancel each other out, and they make no loss. Through this agreement, the economic risk of the loan has been transferred from the second bank to the first. In measuring the risk for the first bank, we would treat this credit derivative as if it were just a loan to the corporation. The example above is very similar to a total return swap except that in a total return swap, a series of fixed payments is made by the first bank rather than an initial lump sum.
In a total return swap, all the credit risk is transferred. However, it is also perfectly possible to write credit-derivatives contracts that have many different structures. For example, if a loan is traded, the payments each month could be equal to the face value of the loan minus the trading price. This would be equivalent to one side paying a fixed amount and in return owning the loan.
Another structure might be that if the corporation defaults, one side pays a fixed amount and the contract terminates. If the fixed amount was set to be equal to the expected loss in the event of a default (LIED), then a bank owning both the loan and the credit derivative would expect to make no loss if the corporation defaulted. However, there is the possibility of the bank making a loss or profit if the actual LIED is different from the derivative payment. Such a derivative would be treated as a loan with a variable LIED minus a loan with a fixed LIED.
Credit exposures to retail customers take generally the same form as exposures to corporations in that they can be structured as loans or lines, and they can be secured or unsecured. Let us briefly review the main characteristics of each type of structure.
Personal loans are typically unsecured and may be used by the customer for any purpose. They are generally structured to have a fixed time for repayment. The interest charges may be fixed at the time of origination, or may float according to the bank’s published prime rate, which the bank may change at its discretion.
Credit cards are again generally unsecured by collateral, but they have no fixed time for repayment. The interest-rate is typically 10% to 15% above the floating prime rate, to compensate for the very heavy default rates experienced on credit cards.
Car loans are the same as personal loans except that they are for a specific purpose and have the car as collateral. They tend to have a lower loss given default than personal loans because of the collateral, and they have a lower probability of default because the customer is unwilling to lose the car.
In a lease, the customer is allowed to use a physical asset (such as a car) that is owned by the bank. Leases are typically structured so that at the end of a finite period, the asset will be returned to the bank. The customer makes regular payments to cover the interest that would have been required to purchase the asset and to cover depreciation. The customer typically has the option to buy the asset outright at the end of the lease for a prespecified lump sum.
Hire-purchase agreements are similar to leases except that the payments include the full value of the asset, and the customer is certain to own the asset at the end of the agreement.
Leases and hire-purchase agreements are similar to car loans in that they are secured by the physical asset that has been purchased. Leases are structured such that the bank continues to own the physical asset legally until all lease payments have been made. This makes repossession easier and reduces the loss given default.
Mortgages use the customer’s home as collateral. This minimizes the probability of default. Furthermore, banks generally ensure that the loan-to-value (LTV) ratio is less than 90%, so even if the property value drops by 10%, the bank will still have a loss given default of 0.
A home-equity line of credit (HELOC) is like a credit card but secured by the customer’s house. This ensures a low probability of default. However, HELOCs are generally subordinated to the customer’s primary mortgage, meaning that in the event of default, the house will be sold and the mortgage will be fully paid off before any payments are made towards the HELOC. This means that the loss given default for a HELOC is much higher than the LGD on the corresponding mortgage.
Loans to corporations are generally large, and correspondingly large amounts of data and analysis are available on each corporation. In contrast, loans to retail customers are relatively small, and only a small amount is known about each customer. However, there are many more retail customers than there are corporations, so the total size of a bank’s retail portfolio is often larger than its corporate-loan portfolio.
Another significant difference between corporate loans and retail loans is that the terms of the agreements between a bank and its customer are much more standardized because of the relatively massive volume of retail customers compared with the number of corporations. This allows retail exposures to be analyzed as a homogeneous mass.
Although there is a relatively small amount of information known about each customer, the average behavior of a large number of customers can be predicted reasonably well. Risk for retail customers is usually estimated by grouping them according to automated credit scores, such as the FICO score, and then gathering historical default and loss data on each group. The FICO score is the score from one of the models created by Fair, Isaac & Company. The model takes credit-bureau information on a retail customer, such as age, income, total number of credit cards, and number of delinquencies in the last three years, and produces a single number, the score. The score generally corresponds to the customer’s probability of default, but models can also be used to predict other aspects of customer behavior, such as the probability of delinquency or the probability of the customer’s actually using a credit card.
Bonds were discussed at length in the market-risk section. The value of a bond depends on the risk-free interest-rate, the credit rating, the spread for that credit rating, and whether or not the corporation issuing the bond has defaulted. Changes in value due to interest-rates and the spread for a given rating are generally treated in the market-risk framework. Changes in the credit grade and actual default are either neglected or treated in the credit-risk framework. One rationale for this is that since bonds are liquidly traded, it is assumed that they can be sold with only a small loss whenever a downgrade occurs, and long before a default.
If the bonds are not sufficiently liquid to be easily sold before a default, they can be treated along with the loans. As with loans, a bond’s credit risk depends on the level of seniority and whether it is secured with collateral.
From this discussion, you may wonder what happens to the interest-rate risk of loans. The interest-rate risk from loans is removed in the ALM transfer-pricing process and is relocated onto the ALM desk, as discussed earlier.
Asset-backed securitization is used with retail assets, such as credit cards and mortgages. In an asset-backed security, the payments from many uniform assets are bundled together to form a pool. This pool is then used to make payments to several sets (or tranches) of bonds. Typically, there will be one set of bonds that is highly rated (e.g., AAA) and one set that is rated lower (e.g., BB). Any residual between the pool payments and the bond payments is typically retained by the institution originating the security. This residual amount is very volatile and is often called “toxic waste.” This is illustrated in Figure 17-1.
If the payments into the pool are insufficient to pay the bondholders, it is possible that some of the bond payments will be less than scheduled. The probability of such underpayment depends on the degree of overcollateralization, i.e., the extent to which the value of the assets is expected to exceed the value of the bonds. The probability of underpayment also depends on the volatility of the value of the assets.
Asset-backed securities have often been used by banks to sell assets nominally to other investors, thereby removing the assets from the official balance sheet of the bank. If the assets are removed from the official balance sheet, the bank no longer needs to hold regulatory capital for the assets. However, if all the tranches of the security are highly rated, and the bank retains all of the toxic waste, then very little of the economic risk has been transferred from the bank. In effect, the regulatory-capital requirement has been reduced, but the economic-capital requirement is unchanged. This is useful to a bank if the market is inefficient, and investors in the bank can only judge the risk by the regulatory capital and cannot observe the required economic capital. In this case, the bank can seem to remain safe, and obtain low-cost funding, while taking large risks and (hopefully) getting large returns.
FIGURE 17-1 Illustration of an Asset-Backed Security
The analysis of the credit risk of an asset-backed security is the same as the analysis of a portfolio of loans. In this case, we calculate the probability distribution of the payments from the pool of underlying assets and use this to estimate the probability that the pool will be sufficient to pay the bonds. The calculation of the probability distribution depends on the risk of the individual assets and the correlation between them. Estimation of this correlation is difficult and is discussed in the later chapter on risk measurement for a credit portfolio.
Securities lending (sec lending) and repurchase agreements (repos) are common functions in trading. From a credit-risk perspective, both sec lending and repos are short-term collateralized loans. In securities lending, a counterparty asks to borrow a security from the bank for a limited period of time. The security is typically a share or bond. To minimize the credit risk, the counterparty gives collateral to the bank that is worth slightly more than the borrowed security. The collateral is typically in the form of cash. At the end of the trade, the counterparty returns the security and the bank returns the cash, less a small amount as a fee.
Repos are very similar to securities lending except that they are used to gain funding. In a repo, a security is sold by the bank with a guarantee from the bank to repurchase it at a fixed price and date. At the time of sale, the bank receives cash. At the time of repurchase, the bank sends the cash back to the counterparty, plus a small additional amount, which is effectively an interest payment for the loan.
In both sec lending and repos, the bank could make a credit loss if the counterparty defaults and the value of the security has risen to be higher than the amount of cash that the bank was expecting to pay to get the security back. The expected exposure at default will be the average amount by which the value of the security can be expected to exceed the cash. This can be calculated from the probability distribution of the security’s value over the life of the deal. For example, Figure 17-2 shows the probability distribution for a security and the value of the cash held by the bank.
The average exposure at default is calculated from the possible exposure, times the probability of that exposure’s happening. The exposure amount is the maximum of zero, or the difference between the security’s value and the cash. Mathematically, the average exposure is the probability-weighted integral of the extent to which the security’s value (V) exceeds the cash value (C):
In the above analysis, we did not specify how to estimate the probability distribution for the security, pr(V). The simplest choice would be to assume that it was a Normal distribution with a mean equal to the current value of the security, and a standard deviation equal to the standard deviation of daily price changes times the square root of the number of days for the transaction. This analysis assumes that the behavior of the security is unaffected by whether the counterparty defaults. This would not be the case if the security was a bond issued by the counterparty. In that case, default and change in value would be highly correlated. Standard good practice is to accept only collateral that is not related to the counterparty, in which case our analysis above is valid.
FIGURE 17-2 Illustration of Average Credit Exposure for a Repo
A margin account is another form of collateralized loan. In a margin account, a customer takes a loan from the bank, and then with the loan and his own funds, purchases a security. The security is then held by the bank as collateral against the loan. The pledging of the security as collateral by the customer to the bank is called hypothecation. It is also possible for the bank to pledge the security to another bank to get a loan. This is called rehypothecation.
Margin accounts are used by customers who want to leverage their position and increase their potential returns. As an example, consider a customer who has $10,000 and takes a loan for $10,000. This is used to buy $20,000 worth of securities. If the price rises by 10% to $22,000 and the customer sells, then after paying back the loan with interest, the customer has a little less than $12,000, a 20% gain. Conversely, if the price falls by 10%, the customer makes a 20% loss.
Typically, retail customers are allowed to borrow only up to half the value of the securities they own. If the value of the securities falls, the bank will ask the customer for more cash to maintain the 50% ratio; this is called a margin call. If the customer does not respond, the bank will sell all or part of the shares. After paying off the loan, any residual value is given back to the customer. If the securities lost more than 50% of their value before they were liquidated, and the customer failed to make up the difference, the bank would suffer a credit loss.
The potential exposure at default is quantified by the probability distribution of the security’s value over the days from the security’s first being worth over 200% of the loan, through the time it takes for the bank to make a margin call, plus the time it takes for the bank to liquidate the position if the customer does not respond. The simplest approach is to assume that the security value has a Normal or log-Normal distribution with a mean equal to the current value (V0) and standard deviation equal to the daily standard deviation of the value multiplied by square root of the time to liquidation. The potential exposure is illustrated in Figure 17-3. The average exposure at default for a 50% margin account is given by the equation below:
If the value is greater than V0/2, the exposure is zero.
FIGURE 17-3 Possible Exposure for a Margin Account
For normal derivatives, credit risk is a by-product of an essentially market-risk transaction. The estimation of credit exposures for derivatives is quite complex and discussed here in three sections: how credit risks arise, how they can be quantified, and how they can be reduced.
The derivatives that we discussed in the earlier market-risk chapters have their values determined according to a market variable, such as the price of an equity or the prevailing interbank lending rate. When trading derivatives, such as swaps and options, there is the possibility, indeed the hope, that over the life of the derivative contract, the market rates will change and the counterparty will owe money to the bank. When this is the case, the derivative is said to be “in the money” to the bank.
As an example, consider the bank being long a call option on an equity. If the value of the equity increases, the bank can exercise the option and receive the highly valued equity in return for the strike price. The bank’s profit would be the difference between the equity price and the strike price. If the counterparty went bankrupt before the option was exercised, the bank would lose this potential profit. If the idea of losing potential profit seems a little obscure, consider what would happen if the bank had also entered into an agreement with another customer to deliver the equity. If the counterparty defaults on the option, the bank will need to use its own reserves to buy the equity for delivery to the customer.
Notice that if the option had been out of the money, the counterparty’s bankruptcy would have had no effect on the bank. In general, there can only be a credit loss if the derivatives contract is in the money to the bank. If it is out of the money, then when the counterparty goes bankrupt, there is no credit loss because the counterparty does not owe the bank anything. In this case, the bank simply pays any remaining amount it owes to the counterparty and closes the contract.
Because the exposure can vary greatly depending on changes in the market, when managing credit exposures to derivatives-trading counterparties, the bank needs to consider not just the current market-to-market exposure, but also the potential future exposure. Returning to the example of the call option, on the day of initiating the option, the mark-to-market value will be close to zero, which would seem to indicate no credit risk, but if equity prices move, there is the potential that the exposure could become very great.
Let us now discuss how credit risk can be quantified for the three most common types of derivatives: vanilla options, FX swaps, and interest-rate swaps.
For a vanilla call option, there is no exposure if the bank has sold the option (gone short). In this case, the bank has received the option premium and now simply has to face the possibility of paying the counterparty if market rates change. If the bank is long the option, there will always be a credit exposure until the contract expires because the option will always have time value. Theoretically, the credit exposure from a call option could become infinite if the value of the underlying went to infinity.
Saying that the credit exposure could be infinity is not terribly useful for managing the credit risk of a derivatives portfolio. Instead, the potential future exposure over the remaining life of the instrument can be better described using statistical measures. The potential credit exposure is usually described in terms of the expected exposure (EE) and the maximum likely exposure (MLE). The expected exposure is the average exposure across all possible market movements, weighted by the probability of the movement. The maximum likely exposure is a measure of how bad the exposure could be, given a certain level of confidence. Typically, the 95% confidence interval is used. This means that we can be 95% sure that the exposure will be less than the MLE.
Both the EE and MLE have a term structure; i.e., the amount changes as we look into the future. As an example, consider a vanilla call option with a strike price close to the current equity price. Over the next day, the price is likely to be only a little higher than the strike price, but over several months, it could become much higher. There is the potential that in a few months’ time, the counterparty could owe the bank a large amount.
For simple instruments with single payments, such as vanilla options, it is relatively easy to calculate the EE and MLE analytically in a closed-form equation. The 95% MLE is the option price if the stock price is equal to the 95% worst case. If we assume that the stock price has a Normal probability distribution, then the 95% worst case is 1.64 standard deviations from the current stock price. The standard deviation over T days is the standard deviation over one day multiplied by the square root of T. For a call option, the MLE T days in the future is given by the following equation:
Here, C[s, t] is the value of the call option with the stock price equal to s, and t days left to expiration. S95% is the 95% worst case stock price, Te is the time from now to expiration, T is the number of days into the future that we want to evaluate the MLE, and σS is the daily standard deviation of the stock price.
The expected exposure (EE) is a little more difficult to evaluate because we need to calculate the value of the call, weighted by the probability density of the stock price:
Figure 17-4 shows a random walk for the price of an equity, and Figure 17-5 shows the corresponding credit exposure for a call option on that equity. Notice that because there is only a single payment, and uncertainty increases as we look further into the future, EE and MLE for a vanilla option keep increasing up to the final settlement date.
FIGURE 17-4 Change in the Price of an Equity Underlying an Option
FIGURE 17-5 Change in the Credit Exposure in an Option Contract
In an FX swap, the parties agree to exchange fixed amounts of each currency on the last day of the contract. If we are based in dollars, and paying D dollars and receiving P pounds, then the value of the swap is the difference in the NPV of each cash flow converted back into dollars:
Here, FXP,D is the spot exchange rate, rP,T is the sterling discount rate for maturity T, and rD,T is the corresponding dollar discount rate. The credit exposure on the swap is the maximum of zero or the value of the swap. For there to be an exposure, the value of the currency to be received should be greater than the value of the currency to be paid. The maximum exposure would occur if the currency to be paid had a massive devaluation. In this case, the value of the currency to be paid would be close to zero, and the credit exposure would be equal to the value of the currency to be received.
A reasonable estimate of the EE and MLE for an FX swap can be obtained by using the parametric-VaR framework to calculate the volatility of the value of the contract, σV. The 95% maximum likely exposure of the swap is then the maximum of 0 or the current price plus 1.64 standard deviations:
The expected exposure is the integral of the positive value, weighted by the probability density of V:
If we assume that the value is Normally distributed with a mean equal to the current value and a daily standard deviation of σV, then the expected exposure is obtained by integrating the Normal probability-density function:
We were able to obtain these neat analytical expressions for EE and MLE because the payment structure was simple and because we made simplifying assumptions about the valuation model and the probability-density function for the random variables. For more complex products or models, we need to resort again to using a simulation tool, such as Monte Carlo.
The measurement of exposure for interest-rate swaps is made complex by the multiple payments and by the complex form of interest-rate movements over long periods. In an interest-rate swap, the parties regularly exchange the difference between a notional amount times a fixed rate, and the same notional amount times a floating rate:
Payment = Nrfix − Nrfloat
For a swap making payment every six months, the floating rate is typically equal to six-month LIBOR plus a spread.
An interest-rate swap is equivalent to one side making payments on a fixed-rate bond and the other side making payments on a floating-rate bond. The value of a swap is therefore equal to the value of a fixed-rate bond minus the value of a floating-rate bond.
The value of a fixed-rate bond is the NPV of the fixed-interest payments, plus the NPV of the final principal payment:
Here, N is the notional amount, rfix is the fixed rate, and tnext is the time to the next coupon payment.
To value a floating-rate bond, we assume that at the next payment date, the required coupon will be paid and the new coupon will be set such that the value of the bond on that day will equal the face value (i.e., the bond will be at par). The total value of the floating-rate bond on the next payment date is therefore equal to the following:
VFloating,tnext = Nrfloat + N
Here, rfloat is the rate that was fixed for the next coupon payment on the floating side. The value of the bond today is the value of the bond on the next payment date, discounted to today:
The value of the swap can then be calculated as follows:
The equation above gives us the value of a swap in terms of the rates of today’s yield curve. This equation can be used in a simulation to estimate the distribution of possible future values for the swap, and therefore the distribution of the possible future credit exposure. The simulation creates a random interest-rate path and then uses the above equation to value the option at each point along the path.
Figure 17-6 shows a scenario for the value of an interest-rate swap, and Figure 17-7 shows the corresponding credit exposure.
By repeating this analysis for multiple scenarios (in this case, 1000) we can obtain an ensemble of exposures from which we can calculate the expected exposure and maximum likely exposure. These are shown in Figure 17-8 for an interest-rate swap that at the initial time (i.e., today) has a mark-to-market value of zero. Notice that interest-rate swaps have the maximum likely exposure approximately one-third of the time from the date that the swap is started to the time when the last payment is made. The sawtooth appearance occurs when interest payments are made and the outstanding exposure drops.
Monte Carlo evaluation takes a long time, so some banks carry out a set of simulations for generic instruments, then store the results in a table. The exposure is then approximated as “mark-to-market plus add-on,” where the add-on comes from the table. The add-on is typically a percentage of the notional amount, and depends on the time left to maturity and the extent to which the derivative is in the money. This “add-on” technique works for single instruments, but does not work well for netting agreements, as discussed in the next section.
FIGURE 17-6 One Scenario of Interest-Rate-Swap Value
FIGURE 17-7 Scenario for Interest-Rate-Swap Credit Exposure
FIGURE 17-8 Expected and Maximum Likely Exposure for an Interest-Rate Swap
In this section, we discuss seven common ways for managing counterparty credit risk:
1. Requiring collateral
2. Settling according to the mark-to-market
3. Early settlement in the event of a downgrade
4. Using a special-purpose vehicle (SPV)
5. A netting master agreement
6. Counterparty exposure limits
7. Pricing for credit risk
If the bank considers that its counterparty has a significantly high probability of default, it can reduce the potential loss by requiring collateral. For example, if the current mark-to-market value of a derivatives contract with a counterparty is $100, the bank may ask the counterparty for $100 in cash to be held as collateral. If the counterparty later defaults on the derivatives contract, the bank will keep the cash, thereby making no net loss. If changes in the market reduce the value of the derivative to $90, the bank would release $10 of collateral back to the counterparty. If the market changes so the value of the contract is negative (i.e., the bank owes money to the counterparty) then the amount of collateral would drop to 0.
Typically, the amount of collateral that the bank requires is equal to or slightly higher than the current mark-to-market value of the contract. The bank will require the collateral to be more than the current value of the contract if the contract value is highly volatile or if the value of the collateral is volatile, e.g., if the collateral is in the form of bonds or equities rather than cash.
Settling according to mark-to-market is very similar to using cash collateral, except that if the value of the contract becomes negative, the bank has to give cash to the counterparty. Settling according to mark-to-market is rare and is only used when the credit risk is very high, for example for a large swap in a project finance deal. (Project finance deals are generally risky because payments depend on the profits from a single project.)
Settling according to mark-to-market reduces the credit exposure, but it increases the cash-flow volatility for the counterparty and may increase the counterparty’s probability of default. The probability of default is affected because the company is forced to pay the full change in value as soon as the market moves, rather than having a series of slightly increased swap payments. This sudden need for a large payment can cause the company to have a cashflow crisis.
A bank can protect itself from the default of a counterparty by adding a clause in the derivatives contract that states that if the counterparty’s credit rating falls at all from its current level, the contract will be terminated and immediately settled at the existing mark-to-market value. To be effective, this requires the rating agencies to identify the need for a downgrade well in advance of any default. Such an agreement is also onerous to the counterparty because in a time of trouble (the downgrade), the counterparty could suddenly be forced to make a large payment to the bank to close the contract.
Derivatives traders want to concentrate on market risks and generally do not want to be distracted by the credit risks of their counterparties. Ideally, they would deal with a AAA-rated counterparty so that default is extremely unlikely. There are relatively few AAA-rated banks, but this problem has been solved by setting up AAA-rated special-purpose vehicles (SPVs) to trade derivatives. An SPV is a separate legal entity. It is set up by a parent bank, and is given a large amount of capital. It is effectively a minibank that only trades derivatives and is fully owned by the parent bank. Although the bank is legally separate, it shares the staff and facilities of the parent bank.
The legal structure is such that in the event of the parent bank’s defaulting, the creditors will not be able make any claims on the SPV. This makes the SPV “bankruptcy remote” from the parent bank and will allow it to continue operating to honor its current derivatives contracts.
A netting master agreement is a legal agreement that covers all the derivatives transactions between two institutions. The agreement states that in the event of default, the bank is only liable for the net amount that it owes the counterparty under all contracts, and not the gross sum. As an example, consider a bank that has bought an option from a counterparty and sold a very similar option to the same counterparty. Assume that the counterparty defaults, and at that time the bank owes $100 for one option, and the counterparty owes $90 for the other option. If there was no netting agreement, the bank would have to pay $100 and then get in line with all the other creditors to try to recover what it could of the $90. However, if the bank has a netting agreement, then the bank only owes the net amount of $10. Under the netting agreement, the bank pays the $10, and then there are no further claims on either side.
Although simple in concept, netting agreements can be legally difficult to enforce. It is also difficult to measure the exposure properly under a netting agreement. The measurement problem arises because the net exposure is highly dependent on the correlation between the value of all the instruments traded between the bank and the counterparty. The normal solution to estimating the net exposure is to net the current mark-to-market exposure with the counterparty, and then add on the gross amount of the individual future exposures as if there were no netting agreement.
A more refined but computationally expensive approach is to use simulation. In using simulation, a scenario is created for market conditions, the value of every transaction is calculated under those conditions, and then the net exposure for that scenario is calculated. By carrying out many simulations, we can calculate the expected net exposure and the maximum likely net exposure.
Another approach to managing credit risk is to accept its existence, but limit the total exposure to any one counterparty. The limits have a term structure to limit the exposure at each point in the future. Typically, the allowed exposure reduces as the bank looks further into the future. The limits are in terms of the maximum-allowed EE or MLE. The allowed limits are compared with the measured EE and MLE of the bank’s current transactions.
As an example, consider Figure 17-9, which shows the exposure profile for three transactions with one counterparty: a loan, an interest-rate swap, and an FX swap. Figure 17-9 also shows the net MLE for the combination of all three transactions. Figure 17-10 shows the allowed limit for the MLE to this counterparty. In this example, assume the loan and interest-rate swap transactions have taken place previously, and now the risk management group is being asked by a trader to approve the new FX-swap transaction. Before allowing the new transaction, the risk management group compares the limits with the net MLE that would occur with all three trades. Figure 17-11 shows the limit imposed on the expected MLE. In this case, the MLE would exceed the limit. Given that the limit will be exceeded, the risk management group could refuse to approve the new trade in its current form, or could increase the limit slightly if they thought that the counterparty was reasonably creditworthy.
For every risk the bank assumes, it should ensure that the shareholders are compensated. This includes the credit risk in the derivatives-trading operation. Using the exposure profiles we discussed above and the credit-portfolio analytics we discuss in later chapters, it is possible to calculate the amount of economic capital to be held for each derivatives transaction. The required return on this capital can then be added to the price of the derivatives contract, for example, by modifying the swap interest rate.
A simplified approach is to decompose the derivative transaction into a pure market-risk component, and a loan of an amount equal to the exposure, then charge the counterparty a credit spread on that loan. The amount of the credit spread would be equal to the spread on a loan to a company of the same creditworthiness.
FIGURE 17-9 Stand-Alone Credit Exposures for a Loan, Interest-Rate Swap, and FX Swap
FIGURE 17-10 Limit of Maximum-Allowed Exposure
FIGURE 17-11 Comparison of Net Exposure with the Allowed Limit
In this chapter, we described the common ways in which credit risk is structured, taking particular note of the factors that affect the probability and amount of loss. In the next chapter, we build the framework for calculating credit risk for a single transaction.