Pricing Vulnerable One-Clique Option In Incomplete Market

Nowadays,the amount of OTC options has already exceeded the trading amount of on-the-spot options,and OTC options are more flexible and more diverse.In addition to the huge characteristics of the over-the-counter market,the development of options has more complicated features.At the same time,many assets in real financial markets are incomplete due to lack of liquidity.Therefore,the risk of default,the impact of incomplete market and the path-dependent option are added to the option pricing model,which has practical significance for investors.Under the Klein model,this paper uses a structured credit risk model to establish a vulnerable one-clique option pricing model.Assume that the stock price and the value of the company's assets are subject to the geometric Brownian motion.Firstly,using the method of measure change,the analytical solution of the one-clique option with default risk in the complete market is obtained.Furthermore,we relax the conditions.In the incomplete market,the total assets of the shorts in the options lack liquidity.The Good Deal Bounds method is used to obtain the Girsanov kernal that generates the upper and lower bounds.Based on the principle of risk-neutral pricing,we can get an analytical solution to the one-clique option with default risk in the incomplete market.