Credit Risk for Derivatives: Methodology
Category: Risk Management in Banking
DERIVATIVE EXPOSURES
Derivatives include currency and interest swaps, options and any combination of these building blocks. Swaps exchange interest flows based on different rates, or flows in different currencies. Options allow us to buy or sell an asset at a stated price. The credit risk of derivatives results from the buy and hold view applicable to over-the-counter instruments since they are not traded in organized markets. For derivatives, the originate and hold policy prevails, and the risk is the potential positive liquidation value of instruments until maturity. Credit risk of derivatives has two salient features:
• It is a two-way credit risk, which shifts from one counterparty to another depending on who owns the positive liquidation value. The liquidation value can be both positive or negative, depending, for example, on the relative values of the paying and the receiving legs of an interest rate swap.
• It is interactive with market risk because liquidation values depend on market parameters.
Current and potential exposures differ. The current risk is the time profile of the liquidation value at the prevailing market conditions. The potential risk is the time profile of the upper bounds of positive exposures, at a given confidence level, obtained by generating distributions of values at future time points. This section deals with the modelling of such time profiles.
The first subsection details the specifics of credit risk for derivatives. The second subsection explains the rationale for the determination of current and potential risk, following the guidelines set by the regulatory or advisory bodies. The third subsection illustrates the implementation of this methodology with simple examples. The last two subsections discuss portfolio effects and the netting of exposures within International Swap Dealers Association (ISDA) contracts, allowing us to reduce the risk by offsetting opposite exposures of different deals within the same ISDA contract.
Credit Risk for Derivatives: Methodology
All derivatives have a liquidation value. The familiar Discounted Cash Flow (DCF) model allows valuation of swaps. The stream of flows includes fixed flows and those indexed on market rates or currency exchange rates. Options have a value which combines the value of the right to exercise plus the payoff under immediate exercise (the difference between the actual value of the underlying parameter and the exercise value).
Credit Risk and Liquidation Values
Derivative exposures are subject to a paradox. They can have both positive and negative values since the liquidation value of a swap is the difference between the values of its two legs. Taking the example of an interest rate swap, we assume that the bank receives the floating rate and pays the fixed rate. Should the floating rate be above the fixed rate, the bank is a net receiver of cash. The liquidation value of its contract is positive. It is an asset. The usual view on credit risk is to value it as the difference between what happens in the case of no default and in the case of default. The bank holds an asset and makes a gain under no default. Under default, it loses this gain.
Since the difference can move from positive to negative, the credit risk is a two-way risk, shifting from one counterparty to the other depending on who owns the positive liquidation value. The bank with the positive liquidation value is the one at risk with the counterparty. If the liquidation value is negative, the counterparty is at risk with the bank. Sometimes, counterparty risk qualifies credit risk for derivatives, suggesting the symmetrical two-way risk exposure.
For options, the risk is different. Options purchased have either zero or positive liquidation values, when they are in-the-money. In this case, the buyer is at risk because the counterparty might default on its obligation to pay if the buyer exercises the option. The seller has no risk since, should the buyer default, since there is nothing to pay to him.
The exposure to credit risk is the positive liquidation value owned by the bank at risk. Hence, credit risk for derivatives is market-driven. This interaction with market movements necessitates modelling of future exposures. Liquidation values fluctuate with markets, being sometimes positive and sometimes negative for swaps.
The Potential Risk and Forward Values
Since the credit risk of derivatives has increased a lot with the development of these instruments, an adequate methodology is required to capture the actual potential risk. Guidelines exist to achieve such objectives1, as described in subsequent subsections.
The issue is to find the future worst-case exposures—or the maximum positive values—given market parameter behaviour. This methodology requires valuing the forward values of these instruments, at all future dates until maturity. These are mark-to-future values, since the potential values are forward values at all intermediate dates between today and maturity. The future exposures are the upper bounds of positive liquidation values, at each time point until maturity, given a confidence level. The methodology generates time profiles of liquidation values, whose shapes depend on the nature of the instrument. Interest rate swaps have bell-shaped exposures, while currency swaps have an ever-increasing exposure with time, as explained in subsequent subsections.
The risk exists for the whole holding period, over which the liquidation value can change drastically with time. According to standard terminology, the current time profile of the liquidation values is the current risk and the possible upward change in value generates an additional potential risk. The overall risk at any point in time is the sum of the current and the potential risks.
Loan Equivalents: Usage and Issues
For implementation purposes, it is not easy to manipulate entire time profiles, so it is a common practice to derive loan equivalents, using the peak or the average exposure over time. Loan equivalents summarize modelled time profiles of exposures. They differ from conventional forfeits, which are crude estimates of future exposures without actually modelling them.
Credit equivalents are in percentage of notional. Conventional forfeits have major drawbacks. They do not capture the real risk of individual transactions, since they rely on conventions. For portfolios of transactions, measuring the risk suggests adding all individual transaction forfeits. This practice ignores offsetting effects. Liquidation values can change in opposite ways within portfolios. Moreover, netting allows us to net positive and negative liquidation values within an ISDA agreement. Without the values and signs of exposures, the individual forfeit system falls short of capturing portfolio effects, netting effects and correlations between the market values of the instruments. Modelling future exposures and how they sum up over a portfolio makes it feasible to use loan equivalents that effectively measure the potential worst-case values and calibrate on the market. For netting agreements, the loan equivalent has to be post-netting.
Calculating Credit Risk Exposure of Derivatives
All derivative transactions have a notional amount that measures the size of the transaction. The notional is the base which, combined with market parameters, determines the interest flows or the currency flows of swaps, or the size of an optional transaction in terms of the underlying. Banks hold such instruments until maturity, which ranges from a few months up to 10 or 15 years.
Exposure and Liquidation Value of Derivatives
Over the long run, the liquidation value of derivative instruments can increase considerably. For example, a currency swap exchanges 1 million USD (the notional) against the equivalent in euros. With an exchange rate of 0.9 EUR/USD, a flow would be valued at 0.9 million EUR, if the exchange took place today. However, if the exchange rate fluctuates, the differential flow changes. If the USD reaches 1 EUR, the buyer of EUR is entitled to a gain of 0.1/0.9 = 0.111 million EUR. This is the amount of the loss if the counterparty defaults. By definition, it is the amount at risk, or exposure. Of course, if the exchange rate varies in the opposite direction, the buyer of EUR has no risk since he owns a negative liquidation value. The credit risk shifts to the counterparty who owns the positive liquidation value.
The same happens with options. The buyer of an option expects that the seller will pay him the difference between the exercise price and the current price of the underlying parameter. The buyer of a cap at 5% with a notional of 1000 000 USD expects to receive the difference between the current interest rate, 6% for example, times the notional. This is an amount equal to 1% x 1000000 USD = 10000 USD for each period. Should the counterparty default, the buyer of the option loses that amount, which is the exposure. The risk exists only when the option is in-the-money. If the option is out-of-the-money, there is no current benefit from exercise. The value drops to the time value of the option. The time value is the discounted value of future possibilities that the option becomes in-the-money between now and maturity. In addition, only the buyer of an option is at risk. He is the one who is entitled to receive some value. The sellers obligation is to pay, which does not generate any credit risk for him.