Option Pricing Based On The Credit Risk

Since1973the option has been developing rapidly, especially in theover-the-counter trading, but the counter party default risk was often neglected, andthe risk is not only a direct cause of the2008financial crisis, but also make somerelating to institutions suffered heavy losses or even bankruptcyconsequences.Therefore, More and more experts began to contain credit risk into theoption pricing.In this paper, I will be considering the classic Black-Scholes pricing ofrisk-neutral principle, to discuss options with how the pricing of credit risk. Intraditional classical Black-Scholes model, based on the real world marketenvironment, expanding its model assumptions, it can be more close to the realenvironment, the classic Black-Scholes pricing formula has been improved. Firstconsider the company’s debt is fixed, the underlying asset price follows a geometricBrownian Motion, how is option pricing when the underlying asset price is less thanthe company’s debt; thus consider corporate debt is random, that the debt follows ageometric Brownian motion. in this case,because of the company’s assets is less thanthe random occurrence of debt of how is option pricing; finally consider payingdividends in both cases the credit option pricing formula. Eventually obtained a creditrisk option pricing formula under three conditions, which the latter two cases is theclassic Black-Scholes pricing promotion. Thereby further enrich the option pricingformula and provide investors with more information.