We study the eff ects of stochastic volatility of defaultable bonds using the first -passage structural approach. In this approach Black and Cox (1976) argued that default can happen at any time. This then led to the development of afirst-passage model, in which a rm (company) default occurs when its value falls to a barrier. In the first-passage model the rm debt is considered to be a single pure discount bond and default occurs only if the rm value falls below the face value of the bond at maturity. Here the firm's debt can be viewed as a portfolio composed of a risk-free bond and a short-put option on the value of a rm. The classic Black-Scholes-Merton model only considers a single liability and the solvency is tested at the maturity date, while the extended Black-Scholes-Merton model allows for default at any time before maturity to cater for more complex capital structures and was delivered by Geske, Black-Cox, Leland, Leland and Toft and others. In this work a review of the eff ect of stochastic volatility on defaultable bonds is given. In addition a study from the first-passage structural approach and reduced-form approach is made. We also introduce symmetry analysis to study some of the equations that appear in option-pricing models. This approach is quite recent and has produced successful results. In this work we lay the foundation of this method. Keywords: Stochastic Volatility, Defaultable bonds, Lie Symmetries. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2009.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/8153 |
| Date | January 2009 |
| Creators | Mkize, Thembisile. |
| Contributors | O'Hara, John G. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
Page generated in 0.0019 seconds