Why simulation?

Monte Carlo simulation is state of the art in market and credit risk measurement. By simulating future market development scenarios, the tool obtains the distribtion of the portfolio values in the future. From that distribution, the tool calculates risk measures, such as exposure at default.

Benefits of market simulation include:

Portfolio effects, such as netting, are automatically taken into account.
Adding new products to the portfolio does not require changes in the calculation algorithm.
High accuracy even with non-linear products, such as barrier and digital options.

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Calculating counterparty exposure

Any OTC financial transaction bears counterparty risk: the risk that the counterparty defaults and becomes unable to fulfill its financial obligations.

Suppose we have a derivative contract (e.g. interest rate swap) with counterparty X. To assess our losses from the default of X, let us assume that if X defaults, we close out our position with X and enter a similar swap with another counterparty. Then, our losses will depend on the mark-to-market (MtM) value of the swap at the moment of default.

If the swap is out of the money for us, then we lose nothing: we close out the swap with X (paying the MtM to X), and enter an equivalent swap, receiving the MtM from the new counterparty. If the swap was in the money for us, we incur losses: we close out the swap with X (but X pays us nothing because they are in default), and enter an equivalent swap, where we are required to pay the current MtM to the new counterparty.

We need to keep a cash reserve to cover our losses from counterparty default. How much do we need to reserve? For example, if we have a vanilla 6 year swap with X, how much can we lose if X defaults? The MtM of a swap changes in time, depending on the interest rates. We cannot predict interest rates in the future, but we can calculate, with a certain confidence, the upper bound of our losses: our exposure to X. For instance, if we say that our potential exposure to X at 95% confidence is 100 euros, it means that if X defaults, then with 95% probability our loss will not exceed 100 euros.

Below is the exposure profile calculated by MarketSimulator for an 6 year receiver swap. The x axis is the time of default, the y axis is the potential exposure to X at 95% confidence. Interest rates were simulated with a 3-factor exponential Vasicek model calibrated to historical data.

Notice the sharp drops in the exposure every half year: they correspond to coupon payments. Each time a coupon is payed, the exposure decreases because there are fewer outstanding payments.

The exposure profile gives us a clear picture of the potential losses. This is useful for calculating capital reserves as well as checking exposure limits for the counterparty.