Credit derivative valuation and parameter estimation for CIR and Vasicek-type models.

Abstract

A credit default swap is a contract that ensures protection against losses occurring due to a

default event of an certain entity. It is crucial to know how default should be modelled for

valuation or estimating of credit derivatives. In this dissertation, we first review the structural

approach for modelling credit risk. The model is an approach for assessing the credit risk of

a firm by typifying the firms equity as a European call option on its assets, with the strike

price (or exercise price) being the promised debt repayment at the maturity. The model can

be used to determine the probability that the firm will default (default probability) and the

Credit Spread.

We second concentrate on the valuation of credit derivatives, in particular the Credit Default

Swap (CDS) when the hazard rate (or even of default) is modelled as the Vasicek-type model.

The other objective is, by using South African credit spread data on defaultable bonds to

estimate parameters on CIR and Vasicek-type Hazard rate models such as stochastic differential

equation models of term structure. The parameters are estimated numerically by the Moment

Method.