Applied Mathematics

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Credit derivative valuation and parameter estimation for CIR and Vasicek-type models.
(2013) Maboulou, Alma Prell Bimbabou.; Arunakirinathar, Kanagaratnam.
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.
Discontinuous Galerkin finite element method for the stokes problem using rectangular meshes.
(2020) Ekpe, Wonder Kudzo.; Arunakirinathar, Kanagaratnam.
Abstract available in PDF.