Pricing Of Options With Credit Risk Under Time-varying Parameters

Options give the holders the right to buy or sell a certain amount of underlying assets for a pre-agreed price at a certain date in the future.As the financial market becomes increasingly active,standard options have been unable to meet the needs of investors.So more and more exotic options have been developed,such as path-dependent options,multi-asset options,compound options,etc.Forward-start options and one-clique options are the path-dependent exotic options.Credit risk or default risk is the risk of default on a debt that may arise from the contracting party failing to make required payments.Nowadays,the over-the-counter market is trading more and more frequently,and investors face increasing credit risk.Therefore,it is significant to price options with credit risk.In this paper,we suppose that the counterparty has liquidity up to the expiration time.On the expiration time,the counterparty will default if its asset value (1is lower than its debt .Additionally,we assume that the underlying asset price and (1follow the stochastic differential equations with many diffusion sources.Under these assumptions,we study the pricing of the standard European options,forward-start options and oneclique options with credit risk.The main results are as follows:Firstly,by using the integral method,we get the pricing formulas of standard European options with credit risk.The results extend the previous related results.Secondly,by using change of measure,we get the pricing formulas of the forwardstart options with credit risk.The pricing formulas of the forward-start options without credit risk and the standard European options pricing formulas with credit risk are the special cases.Thirdly,by using change of measure,we get the pricing formulas of the one-clique options with credit risk.The pricing formulas of the one-clique options without credit risk is a special case.