The Valuation Of Barrier Option Subject To Credit Risk

With the need to hedge risk ,many options are traded over-the-counter between financial institutions or institutional investors. As they are not backed by the guarantee of a clearinghouse or an exchange and each counterparty is exposed to the credit risk of the other party, In fact most of them embed the credit risk. Johnson and Stulz(1978) called this option as vulnerable option. This is the credit risk that is no consideration by Black and Scholes in 1973. In addition, Many contracts can be as the derivatives contracts with credit risk. For example, insurance contract is such derivatives contracts. In short, as long as the payment of the options is not backed by the guarantee of a clearinghouse or an exchange ,they can be as the financial options with credit risk.This article deduce the pricing formula of barrier option with credit risk.Chapter 1 is introduction that introduct the development of the theory of option pricing with credit risk. Chapter 2 give the prior knowledge that is used in this article,include the basicconcept of options,the basic concept of barrier options and mathematical for option----Stochastic Processes and Stochastic Analysis.Chapter 3 deduce the pricing formula of Europe option with credit risk which assumed the debt and the risk-free rate r is constant. First, using the martingale to deduce the pricing formula of Europe option,then, using the probability to deduce the pricing formula of Europe option with credit risk.Chapter 4 deduce the pricing formula of barrier option with credit risk which assumed the debt and the risk-free rate r is constant. First, giving the the pricing formula of barrier option,then, using the pricing method of multiple and PDE to deduce the pricing formula of barrier option with credit risk.Chapter 5 aggregate the paper and raise further research direction.