Research On Pricing Of Convertible Bonds Based On PDE Method

With the development of the bond market, there were a variety of derivatives on the bond market. For example, convertible bonds and else. Convertible bond was a hybrid financial products and raised in the 1970 s or 1980 s. Currently, it has become one of hot topics in the study of China’s securities market. How to pricing convertible bonds reasonability become an important topic. In this paper, we studied convertible bonds pricing from multiple angles, and considering the condition of the credit risk of guarantee party, investment strategies and risk appetite of the investor. The final we will expand the utility indifference model and applied to P2 P pricing.First of all we introduced the main research methods for pricing convertible bonds and the status quo.The second chapter presented the basic model used in this paper preliminary knowledge.In the third chapter, we studied convertible bonds pricing from the perspective of investors under the background of credit risk of guarantor. The default process of the bond issuer and guarantor are assumed to be a poisson process, and we consider the stock price jumps after the issuer default, through the hedge we get the party differential equation model and the explicit solution. Finally, we calculated and analysed the effect of various parameters on the model.In the fourth chapter, considered the reality of the financial market is incomplete and investor’s investment risk is not hedged completely, so the degree of investor risk appetite would has a important influence on contingent claim pricing. This section we use the utility indifference principle analysis of convertible bonds pricing in the framework of structural model. Investors could buy convertible bonds, risky assets and risk-free asset, and the risk assets meet CEV process. The goal was to maximize the expected terminal value of wealth of investors by choose the optimal investment proportion. To solve this problem, We deduced two HJB equations for not investment and investment of convertible bonds by the method of utility indifference. Finally we concluded the utility of price difference of the bond by separating of variables Hopf transform.In the fifth chapter, we expanded the utility indifference model and applied to P2 P pricing in the framework of the reduced model. Investors expected utility maximization goal was terminal wealth, and the debtor were considerer in the model of credit risk. We get two HJB equations by considering investors to buy and not buy P2 P. Finally we concluded the utility of price difference of the P2 P claim and analyzed the influence of different parameters on bond prices.The conclusion and prospect in chapter six given the inadequate of the paper and the future research direction.