Pricing Of The Vulnerable Binary Option Under O-U Process

As a kind of financial derivatives, option plays an important role in the financial markets. Therefore, an accurate and effective pricing of op-tion is very important. In the 1970s Black and Scholes put forward the famous Black-Scholes option pricing model. The model had a profound impact for traders about how to price and hedge options, and promote the development of financial engineering. However, with the fast devel-opments of the financial market, the inherent defects of Black-Scholes option model began to emerge, witch restricted the further development of options market. The credit risk in the process of options trading is one of the most obvious defects.Hence, how to adjust the option Prices to reflect the counter party credit risk has become a serious problem,witch is the so-called vulnerable option pricing problem.On the basis of the structure model of vulnerable options, this paper assume that the underlying assets,the value of the company, the company liabilities are subject to O-U process, interest rate is stochastic process. The martingale approach and acturial approach are applied respectively to price the vulnerable binary option.