Credit risk used to be primarily a concern of banks, fixed income investors, and businesses that extended credit as part of their business. The growth of derivatives markets during the 1990s introduced new forms of credit risk, not only for the derivatives dealers who made markets in them, but also for the corporations who used them. Not all derivatives entail credit risk. For example, futures are traded on exchanges that employ a system of margining that virtually eliminates credit risk. However, most OTC derivatives entail credit risk for one or both parties to the transaction. If a dealer sells a corporation a call option, the corporation pays the dealer a premium and faces the risk that the dealer may fail to perform on the option in the event the corporation exercises it in-the-money. If, on the other hand, the dealer enters into an interest rate swap with the corporation, no premium is paid, and the swap starts off with no market value (except, perhaps, that due to a bid-ask spread charged by the dealer). Depending upon fluctuations in interest rates, the swap could take on a positive market value for either the dealer or the corporation. Accordingly, both face credit risk due to the possibility that the swap might come to represent a net obligation of the other party. OTC derivatives actually entail two forms of credit risk:
Settlement risk entails a number of unique issues. In this article, we focus on pre-settlement risk. Many OTC derivatives are structured with termination features. These provide for the immediate termination of the contract should a specified trigger event occur. Trigger events might include:
When a trigger event occurs, the contract is terminated (either automatically or at the option of the other counterparty) and there is an immediate cash settlement between the counterparties for any market value of the contract. Accordingly, a pre-settlement default might entail the following elements:
Unlike settlement risk, which entails exposure equal to a counterparty's gross obligation, pre-settlement risk entails exposure equal to a counterparty's net obligation on that contract. Suppose an institution enters into a forward contract to exchange 1MM GBP for 1.5MM USD in three months. Settlement risk exposes the institution to a possible loss of $1.5MM. Pre-settlement risk exposes the institution to just the difference in market value between the USD and GBP payments. If the pound were trading at 1.45 USD/GBP at the time of a default, this would translate into a loss of just USD 50,000. Replacement cost is a basic metric of credit exposure due to pre-settlement risk. It is the cost that an institution would incur if a counterparty completely defaulted on its obligations. Effectively, it is the cost to the institution of having to completely replace all contracts with that counterparty. Current replacement cost (called mark-to-market exposure) is the replacement cost of a portfolio of contracts with a counterparty based upon those contracts' current market values. Replacement cost is distinct from market value for two reasons:
For example, suppose that an institution has two contracts with a counterparty which have the following market values:
If there is not an enforceable netting agreement between the two parties, the replacement cost of the portfolio is $3MM. This is because, if the counterparty were to default, the institution would still have to perform on its $5MM obligation. The only contract that would be affected by the default would be the $3MM contract. Accordingly, the institution has $3MM at risk.
If, on the other hand, there is an enforceable netting agreement, the replacement cost is $0. In the event of a default, the two obligations would be netted, and the institution would be obligated to the counterparty for $2MM—the same net obligation it has without a default. Accordingly, depending upon whether there is a netting agreement, the replacement cost is either $3MM or $0. Each result is different from the portfolio's market value of –$2MM. Replacement cost can also be measured prospectively. Future replacement cost is the discounted value of the replacement cost of a portfolio of contracts with a counterparty, based upon what those contracts' market values would be under a specified market scenario. Obviously, the result depends upon the assumed scenario. Statistical risk measures such as expected credit exposure summarize what future replacement cost may be based upon the entire probability distribution of possible market scenarios. Suppose an institution is about to enter into a foreign exchange forward contract with a counterparty. With such a contract, the initial market value is zero—except, perhaps for a bid-ask spread. Accordingly, its current replacement cost (or mark-to-market credit exposure) is zero. This, however, gives no indication of the potential credit exposure from the contract. As the underlying exchange rate fluctuates, the contract could take on a positive replacement cost. Indeed, if the exchange rate moves significantly in the institution's favor, the replacement cost could become quite large.
When that happens, it will be too late for the institution to start managing its credit exposure to the counterparty. The time to do so is now—while the institution is still negotiating the contract. Only now can the institution decide whether or not to enter into the contract. Only now, can it incorporate credit enhancements into the deal. The institution cannot base its actions on the mark-to-market credit exposure of the contract, which is zero. Somehow, it must analyze the potential credit exposure. There are two statistical measures of potential credit exposure that are commonly used. They are closely related:
Let's consider our example of the institution which is about to enter into a foreign exchange forward. Exhibit 1 illustrates the probability distribution for the replacement cost, one month from today, for the contract.
The probability distribution in Exhibit 1 is a mixed distribution having two components. The first component is a discrete block of probability corresponding to a zero replacement cost. This probability arises from the possibility that the exchange rate may move against the institution over the next month. In that event, the institution will owe the counterparty money on the contract, and the replacement cost will be precisely zero. The second component of the distribution is continuously distributed, starting at a zero replacement cost and extending beyond USD 1MM. This corresponds to the possibility that the exchange rate may move in the institution's favor. If this happens, the contract will have a positive replacement cost equal to the present value of its market value. Exhibit 2 illustrates both expected exposure and maximum likely exposure (calculated as a .975-quantile of replacement cost) for this example. Expected exposure is simply the mean of the distribution. The maximum likely exposure is the dollar value such that there is a 97.5% probability that the replacement cost will be less than that value—it is the "maximum likely exposure" in the sense that there is a 97.5% probability that replacement cost will not exceed it.
Obviously maximum likely exposure is not literally the maximum value that the replacement cost could possibly take on. For example, when it is measured as a .975-quantile, there is a 2.5% probability that the replacement cost will actually exceed the maximum likely exposure. The term potential exposure is used to refer to expected exposure, maximum likely exposure or any similar metric of possible future exposure. In complex portfolios, with multiple contracts maturing or paying cash flows on various dates, potential credit exposure can vary significantly from one horizon to the next. Specifically, this means that expected exposure and maximum likely exposure are horizon-specific notions. A portfolio does not have a single expected exposure or maximum likely exposure. Instead, those measures of exposure will vary for a portfolio depending upon which horizon they are calculated over. Accordingly, exposure is typically calculated for multiple horizons. In our example, we analyzed potential credit exposure at the one-month horizon. Suppose, however, that the forward contract in that example is going to mature in 6 months. Exhibit 3 illustrates how our analysis might be performed for each monthly horizon, out to 6 months.
Exhibit 3 analyzes maximum likely exposure at each horizon (expected exposure could be calculated similarly). At each horizon, the probability distribution for the contract's replacement cost is determined. For example, the distribution for the one-month horizon is precisely the distribution we constructed in Exhibit 1 above. Here, we are just expanding that analysis to multiple horizons. In Exhibit 3, as the horizon increases, the continuous component of each distribution becomes flatter and more spread out. This reflects the increasing uncertainty in the future value of the contract's underlying exchange rate over greater horizons. The .975-quantile is determined for each distribution, and the results are plotted on a graph. That graph, expanded in Exhibit 4, plots maximum likely exposure as a function of horizon. As we might expect, the potential exposure from the contract increases with horizon.
In Exhibit 4, maximum likely exposure peaks out at $2.3MM at 6 months—just prior to the maturity of the contract. This reflects the fact that exchange rates are likely to move more over 6 months than over a shorter interval. Exhibit 5 shows a similar analysis for a 5-year interest rate swap. The evolution of maximum likely exposure is very different from that of the foreign exchange forward.
Two competing forces shape the evolution of exposure in Exhibit 5:
Actually calculating potential exposure can be an involved process that often requires some form of Monte Carlo simulation. The process is made more complicated by the fact that credit exposures are not additive. It is not possible to calculate exposure for the individual instruments in a portfolio, and then sum the results. For example, suppose an institution has two foreign exchange forward contracts with a counterparty, and that the 3-month expected exposure under each is USD 5MM. Without knowing anything more about the situation, we cannot judge what the total 3-month exposure is for the two contracts. The answer could range from USD 0MM to USD 10MM—or anywhere in between. For example, if there is a netting agreement, and the two contracts are identical, one long and the other short, then their credit exposures cancel, and the total exposure is USD 0MM. On the other hand, if they are both long, the total exposure is USD 10MM. A more complex situation would be if one contract were linked to the EUR and the other to the GBP. Taking into account the correlations between the two exchange rates, the total exposure might be USD 8MM. Accordingly, when Monte Carlo simulation is used to measure credit exposure, it must be applied to the entire portfolio at once. In practice, OTC derivatives are often collateralized, with one or both parties posting collateral whenever they have a net obligation on the derivative. Collateral is typically adjusted daily so that its market value always exceeds that of the derivative. With such an arrangement, net expected exposure and net maximum likely exposure can both be assumed to be zero.
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