New recipes for estimating default intensities

Abstract

This paper presents a new approach to deriving default intensities from CDS or bond spreads that yields smooth intensity curves required e.g. for pricing or risk management purposes. Assuming continuous premium or coupon payments, the default intensity can be obtained by solving an integral equation (Volterra equation of 2nd kind). This integral equation is shown to be equivalent to an ordinary linear differential equation of 2nd order with time dependent coefficients, which is numerically much easier to handle. For the special case of Nelson Siegel CDS term structure models, the problem permits a fully analytical solution. A very good and at the same time simple approximation to this analytical solution is derived, which serves as a recipe for easy implementation. Finally, it is shown how the new approach can be employed to estimate stochastic term structure models like the CIR model.