Extended saddlepoint methods for credit risk measurement

ABSTRACT We propose a new method that extends the saddlepoint approximation to allocate;credit risk. This method applies a Taylor expansion to the inverse Laplace transform;around an arbitrary point to characterize the loss distribution of a portfolio. It is based;on Hermite polynomials. From a computational point of view, our method is less;demanding than other approximate methods. We also extend the current saddlepoint;methods to deal with random recoveries and market valuation. Considering a portfolio;that includes Spanish financial institutions, we show that these extensions can characterize;the risk of the portfolio very well. The risk allocation method generates more;accurate results than other approximate methods, with few calculations for default;mode models and pure macroeconomy driven recoveries. We also find that modeling;mixed idiosyncratic and macroeconomic random recoveries does not generate;much greater risk than a pure macroeconomic random recoveries model. Finally, the;results for the market valuation approximation are also very accurate, but this method;requires a higher number of calculations. Other methods, such as the Monte Carlo;importance sampling one, may be more suitable.