Valuing Corporate Bond And Its Derivative Based On A Jump-diffusion Model

The Chinese bond market has been developing rapidly since the financial reform.Among which,the corporate bond is a vital component.On the other hand,since the rigid payment is being broken up nowadays,the importance of valuing the defaultable debt and its derivative accurately increases a lot.In this article,the author does the literature review for the research of valuing corporate debt and credit default swap during the last tens of years.From the micro perspective,the stock of the corporation which issues only bond and stock could be regarded as a European call option,whose underlying asset is the total asset of the corporation,while the strike price is the amount of total debt.Thus,the corporate debt could then be regarded as the total asset together with a short position of that call option.Therefore,we could introduce the option pricing theory into the valuing of corporate debt.The structural approach from the articles of Robert C.Merton,Francis A.Longstaff and Eduardo S.Schwartz is the representative of the theory.It is noted that in the Black-Scholes option pricing theory,it is assumed that the underlying asset follows the geometric Brownian motion,which means its path is continuous.However,it is not always true for the corporation in practice.The research also proves that the solution under the continuous model could not explain some phenomenon of the real market.Therefore,it is essential to introduce the discontinuous process into the model.Robert C.Merton introduced the jump-diffusion model into the option pricing theory,while the models of Chunsheng Zhou,Masaaki Kijima and Teruyoshi Suzuki are based on Merton's and are adapted to fit the real market.In this article,the author conducts an analysis for the sensitivity of the parameter related to the jump component in the model of Zhou.Therefore,the author draws a conclusion that the model does have some advantages in the bond pricing problem.There is another vital instrument in the bond market,called credit derivative,whose underlying asset is defaultable debt.In the end of 2016,the Chinese interbank bond market formally introduced the credit default swap.In the future,this market would become more and more critical with no doubt.In this article,the model of Ruicheng Yang,Maoxiu Pang and Zhuang Jin is introduced,which applies the jump-diffusion model under the double exponential distribution and comes up with the numerical solution of the price of credit default swap.