Credit Exposure Modelling

Credit risk, like all risk, consists of two identifiable parts: exposure and outcome – how much is owed and will it be paid? Uncertainty in credit risk can be addressed using counterparty default probabilities. These probabilities cannot be directly observed, but are usually inferred from credit ratings and longer-term trends. The higher the probability of default, the greater the credit risk.

Credit exposure to a counterparty is the amount lost when the counterparty fails to meet its financial obligations, i.e. when it defaults. Credit exposure depends on the value of transactions (e.g. swaps, loans and other securities which introduce credit risk) entered into with the counterparty, and taking into account any master agreements specifying netting rules between the parties involved. Unlike outcome, credit exposure does not depend on the default probability of the counterparty. The greater the size of the transactions or investments entered into with a single counterparty, the greater the credit risk.

In the simplest case, a transaction consists of only one cash flow, such as the purchase of a certificate of deposit. Here, the credit exposure equals the discounted principal. This is the amount that the lender stands to lose if the counterparty (borrower) defaults. However, it is not possible to give one specific number for credit exposure. For example, if interest rates are assumed to be changeable, the discount factor and discounted principal will also be subject to fluctuation, and consequently, the credit exposure of the certificate of deposit is not absolute.

Relevant risk measures for credit exposures that are sensitive to market movements can be derived from the probability distribution of the contract. These include expected credit exposure (for a certificate of deposit, expectation of the discounted principal) and 95% Value-at-Risk level of credit exposure. This calculation provides an expected level of credit exposure that is unlikely to be exceeded within the given time horizon (i.e. in 95% of cases this level will not be exceeded).

Market variables can have a very large effect on the credit exposure of a swap contract. Indeed, in adverse market conditions, the swap could lose all of its value and therefore lose all of its credit exposure. Similarly, if the market value moves favorably, there is an increase in credit exposure due to a larger potential loss in the event of default. Expected credit exposure is calculated from the probability distribution of the swap market value, but only where the swap has inherent value.

The first step in calculating credit exposure of a counterparty is to use a risk engine to run a simulation of the possible values of relevant market variables. This could be achieved through Monte-Carlo simulation or historical simulation, if appropriate. Examples of market variables include exchange rates, interest rates, yield curve parameters and equity prices. The simulation can produce a joint distribution of market variables taking into account correlation effects.

The second step is to find the market value distribution of all transactions with the counterparty. This step involves interpolation of yield curves, pricing securities and use of valuation formulae. The distributions give information about the market risk exposure of contracts. The credit risk exposure of a contract can be directly observed as the positive side of its market value distribution. (Positive values correspond to payments (expected) from the counterparty.)

The third step is to calculate the credit exposure to the counterparty. A simple approach is to find the sum of all receivable cash flows from the counterparty (i.e., the amount lost in the event that the counterparty defaults). This approach neglects the effect of netting rules imposed by master agreements and therefore can result in a conservative credit exposure estimate.

A master agreement defines a set of transactions whose payable cash flows can be netted against the receivable cash flows if the counterparty defaults. For this reason, an accurate credit exposure estimate requires a net value be calculated for all contracts that are covered by a common master agreement. The sum of payable cash flows can be subtracted from the sum of receivable cash flows. The net receivable cash flows are added to the total credit exposure of the counterparty.

All the features discussed above are readily available in R/V Platform and SWAP+, the simulation-based tools for financial risk management provided by CD Financial Technology. SWAP+ is designed to capture credit risk exposures caused by counterparties of a financial institution. R/V Platform provides a complete solution for the management of market, credit and liquidity risk, and for regulatory compliance.

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