Calibration of a Stochastic Model for Corporate Credit Spreads
Dr Douglas McLean (Moody’s Analytics, Edinburgh)
Wednesday 23rd September, 2015 14:00-15:00 Maths 325
Within an economy, “corporate credit” is the asset class describing the excess return (or spread) one receives in compensation for purchasing a corporate bond over a government bond with all other aspects of the contract otherwise the same. We introduce a model for corporate credit defaults which is described by a system of seven coupled stochastic differential equations. Of interest to us is the inverse problem of parameter calibration. We demonstrate the calibration problem first to market data in the form of historical US credit spreads by means of a regularisation technique. Secondly, we consider calibration to unconditional “stylised” targets specified in terms of spread moments. Calibration to in-house targets is our preferred technique but necessitates the calculation of modelled moments which is a non-trivial problem. We extend the COS method of Fang & Oosterlee (2008, SIAM Journal on Scientific Computing 31 (2), 826-848) to reduce the intractable problem of evaluating seven and higher dimensional integrals to tractable one- and two-dimensional integrals thus avoiding the necessity for computationally intensive Monte-Carlo simulations. Time permitting, we will discuss the calibration method to our stylised targets.