The saddlepoint method and portfolio optionalities

Richard Martin describes the application of saddlepoint methods to the calculation of tranche payouts and expected shortfall in loss distributions. Aside from computational use in their own right, the resulting formulas motivate a forthcoming discussion on systematic and unsystematic risk in portfolios

This short communication describes the application of saddlepoint methods in the calculation of tranche payouts and expected shortfall (ESF, also known as conditional value-at-risk) from the distribution of portfolio losses. These are closely related quantities that are fundamental to the valuation of collateralised debt obligation tranches (Andersen, Sidenius & Basu, 2003) and credit portfolio management (Martin, 2004). Whereas the density and tail probability are well understood, the latter