New recipes forestimating defaultintensities

This paper presents a new approach to deriving default intensities from CDS or bond spreadsthat yields smooth intensity curves required e.g. for pricing or risk management purposes. Assumingcontinuous premium or coupon payments, the default intensity can be obtained by solving an integralequation (Volterra equation of 2nd kind). This integral equation is shown to be equivalent to anordinary linear differential equation of 2nd order with time dependent coefficients, which isnumerically 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 simpleapproximation 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.