A Few Class Has A Default Risk Option Pricing Model

Containing the credit risk of the option is called vulnerable options.It was proposed firstly by Johnson and Stulz. Credit risk is also known asdefault risk, It is possible to loss that trading party because the otherparty occur default or contract can not be fully perform. Credit risk isone of the major financial risks.Nearly90percent of the derivatives are over-the-counter (OTC) infinancial derivatives.OTC financial derivatives and centralized clearingand settlement in the exchange of products are different, It has nothird-party clearing organizations. So it is important to study that thepricing problem for options with default risk in the OTC market. This thesisbased on the the kein model of a class of vulnerable options pricing.1、 Constant volatility in the the kein model is improved stochasticvolatility. The mathematical model for pricing vulnerable options wasestablished by PDE method. The pricing equation was derived. Then,the numerical algorithm was given by using the finite differencemethod. Finally, the numerical solutions and parameters were analyzed.2、 Considered the pricing problem for quanto options withcounterparty default risk. The mathematical model for pricing quantooptions with vulnerable options was established by PDE method underthe framework of the fixed and floating exchange rate. The pricingequation was derived. Then, the numerical algorithm was given byusing Monte Carlo method. Finally, the numerical solutions andparameters were analyzed.3、 Considered the pricing problem for rainbow barrier options withcounterparty default risk. The mathematical model for pricing rainbowbarrier options with vulnerable options was established by PDE method.The pricing equation was derived by eight rainbow barrier options withdefault risk. Then, the numerical algorithm was given by using the finite difference method.