The Valuation Of Options Subject To Credit Risk

The foundation of financial transaction lies in the credit. So thepossibility of violation, namely the credit risk, influences self-evidentlypeople's financial transaction activities. For a long period of time, thecredit risk has not been payed more enough attention to. However, sincethe 1990s, with the structural transform of global finance system,especially the development of all kinds of OTC derivatives, the credit riskhas attracted much attention of financial market participants and theresearchers both inside and outside of bank systems. The majority ofliteratures regarding credit risk had paid attention to the pricing of debttools such as debenture bond, loan or mortgaged loans, but had generallyneglected the credit risk of OTC financial derivatives. Therefore,developing a model to quantify the influence of credit risk on derivativesis extremely significant. This article attempts to introduce the credit risk to option pricing,with the reference of Black-Scholes risk neutral option pricing andDelta hedging skill, through the partial differential equation approach,we got an option pricing formula subject to credit risk. The main pointsof this paper are as follows: First, we simply introduced the principle ofstochastic process, the B-S pricing method of standard option as well asthe option nature. Secondly, we deducted the differential equationmodel of option pricing subject to credit risk on the base of certainassumptions, and solved the vulnerable option pricing formula fromthis model. Thirdly, in view of the unreasonable assumptions of fixeddefault threshold and fixed interest rate in the above model, wemodified the model, and deducted separately inferred option pricingmodels subject to credit risk under the assumptions of invariable defaultthreshold and the stochastic interest rate as well as the threedimensional array of difference stable solution of partial differentialequation model when the invariable default threshold assumptioncontains two terms. Finally, on the basis of the above models, weanalyzed the influential factors with an approach of numeral examplesand made a comparison with that of standard option prices.This article will be helpful to enrich the study of pricingderivatives subject to the credit risk, and help the participants of OTCderivatives market or other securities market including option structure to assess the influence of credit risk exactly, and hence to promote thedevelopment of OTC financial market theatrically.