The Pricing Of European Vulnerable Option With Jump Risk Value

Credit risk is a kind of risk in financial market which is difficult to carry out quantitative analysis and management.Credit derivatives have been rapidly developed and sought after by investors,since it was proposed in 1992.However,OTC(OTC)shares the majority of derivatives trading.Owing to the absence of a specific regulatory agency in the OTC market,the possibility of the credit default risk is significantly increased.When the call option is exposed to both market risk and credit risk,the option containing these two risks is considered as a vulnerable option.In real life,the company's assets are usually reported quarterly.In order to better describe the option writer's assets,the third chapter of this paper presents a pricing model of vulnerable options under incomplete information.According to the jump diffusion assumptions about the underlying stock price and firm values,a closed-form valuation formula is derived for European vulnerable options under incomplete information.Numerical experiments are used to compare the option value under the incomplete information with three classical option models: the B-S model,the Merton jump diffusion model and the Klein model.In recent years,Markov-modulated regime-switching model is very useful to explain the macroeconomic changes,such as economic structural adjustment,market economic system change and business cycle.In the market economy,interest rate,exchange rate and stock returns are all related to the changes of the economic cycle and the market economy system.Therefore,the study of option pricing based on regime-switching is more close to the actual market.The financial market under the assumption of regime-switching model is usually incomplete,the equivalent martingale measure is not unique,so how to construct and select the equivalent martingale measure is also an important part of this paper.In the fourth chapter,we consider the pricing problem of European vulnerable option in terms of the value of the underlying stock and the value of the asset of the option in the Markov-modulated jump-diffusion model.On the research of option pricing,jump risk is usually divided into two categories,one is to regard the jump risk as a systemic risk,which can be hedging;one is to regard jump risk as a non system risk,which cannot be hedging.In this chapter,we consider the jump risk as a systemic risk and can be hedged,so we need to consider the pricing of jump risk value when transform the original measure to the risk neutral measure.On this basis,we also study the pricing of the option without considering the jump risk value and the same jump risk value.In order to find the impact of the jump risk value of the vulnerable options,we also studied the vulnerable options without considering the jump risk value and the vulnerable options with the same jump risk value.