A Joint Term Structure Model for Credit and Interest Rate Risk with Flexible Correlation Structure

Uwe Schmock (Vienna University of Technology, Austria)

Abstract: We propose a novel defaultable term structure model that is capable of capturing negative instantaneous correlation between credit spreads and risk-free rate documented in empirical literature while sustaining the positivity of the default intensity and risk-free rate. Given a multivariate Jacobi (or Wright–Fisher) process and a certain functional, we are able to compute the zero-coupon bond prices, both defaultable and default-free, in a relatively tractable way by using the exponential change of measure technique with the help of the "carré du champ"operator as well as by using the transition density function of the process. This density is derived from the dual process representation of the multivariate Jacobi process, which also enables exact simulation of the evolution of bond prices. The bond price formula is a series involving ratios of gamma functions and fast converging exponential decay functions. The main advantage of the proposed reduced form model is that it provides a more flexible correlation structure between state variables governing the (defaultable) term structure within a relatively tractable framework for bond pricing. Moreover, in higher dimensions one does not need to rely on numerical schemes related to the differential equations, which may be difficult to handle (e.g multi-dimensional Riccati equations in affine and quadratic term structure frameworks). Time permitting, illustrations and applications will conclude the talk. (Joint work with Sühan Altay.)