Pricing Of Vulnerable Options In Stochastic Financial Markets

Vulnerable option refers to an option that is affected by credit risk in the over-the-counter market.Credit risk is more likely to occur because of the lack of effective supervision of over-the-counter market.However,in actual transactions,the factors of affecting option pricing are also influenced by many market parameters.Therefore,based on the Klein model,this paper takes the factors including variable interest rate,jump risk and dividend in over-the-counter market into consideration of the pricing of European vulnerable options,and finally analyzes the influence of various factors on the pricing of European vulnerable options through simulated numerical experiments.The main content of this paper is to study the influence of various market parameters on the pricing of European vulnerable options in the stochastic financial market.It consists of the following five parts:First of all,we described research background and significance of this paper,then we sorted out the current domestic and foreign related research status and summarized the content and structure of the paper.Secondly,we study the influence of variable interest rate and jump risk on pricing of European vulnerable options.We assumed that the risk-free interest rate changes with a deterministic function,and based on the underlying stock price and company value obeying the jump diffusion process,we obtain the JD-SV,JD-S and JD-V option models of European vulnerable option pricing.Jump in the firm value significantly increases the possibility of default and reduces the price of European vulnerable options.Finally,the value of options under the four options models of JD-S,JD-V,JD-SV and Klein model is compared by numerical experiments.Once more,assuming that the underlying stock price volatility as stochastic process on the basis of assumptions risk-free interest rate being a deterministic function change,the approximate solution of European vulnerable call option pricing was deduced.Moreover,we give numerical example which discusses the influence of stochastic volatility and window average interest rate on European vulnerable call option prices.And then,assuming that the stock price and the value of the company are continuous dividend payments,we obtained European vulnerable option pricing formula by Mellin transform analysis method with continuous dividends paid under incomplete information,Finally,we analyzed the impact of dividend yield on pricing of European vulnerable options by numerical example.Finally,we summarized the research results of this paper.At the same time,the deficiency and the aspects of this paper that can be improved are given.