The saddlepoint approximation formulas provide versatile tools for analytic approximation of the tail expectation of a random variable by approximating the complex Laplace integral of the tail expectation expressed in terms of the cumulant generating function of the random variable. We...

Numerical calculations of risk measures in credit risk models amount to evaluation of various forms of tail expectations of portfolio loss distribution. Though the moment generating function of the loss distribution in CreditRisk+ model is available in analytic closed form, efficient, accurate...

The numerical calculations of marginal risk contributions associated with the two risk measures, Value-at-Risk and Expected Shortfall, pose challenges due to the rare event character of multiple defaults among obligors in credit portfolios at a high confidence level. We explore various...

The numerical calculations of marginal risk contributions associated with the two risk measures, Value-at-Risk and Expected Shortfall, pose challenges due to the rare event character of multiple defaults among obligors in credit portfolios at a high confidence level. We explore various...