Pricing Convertible Bonds Under A Markov-modulated Jump Difusion Model

Along with the integrity of financial market, financial derivatives are emerging in an endlessstream. The pricing problem has become aroused great concern of the scholars and financialworkers. Since convertible bonds have been an important financing derivatives in the financialmarkets, how to price becomes very important. In practice, the market economy is either stablestate or high volatility state. As for this phenomenon, we assume that the price process of riskyasset follows a two states Markov-modulated jump process, the risky asset price is driven by aBlack-Scholes model when the market is stable, and the risky asset price follows a jump difusionprocess when the market state is high volatility. We consider the pricing problem of convertiblebonds under this financial model.The thesis is arranged as follows:Chapter1In this chapter, we introduce the backgrounds and development of convertiblebonds pricing and Markov-modulated model, and introduce the basic knowledge. Finally, weintroduce the main work of this article.Chapter2In this chapter, we assume that the price process of risky asset follows a twostates Markov-modulated jump process, and obtain the value formula of convertible bonds underMarkov-modulated jump model by measure change and no arbitrage pricing method. In addi-tion, we give the numerical solutions of the convertible bonds under the Black-Scholes model andthe jump difusion model and Markov-modulated jump model by using Monte Carlo simulationmethod.Chapter3Based on the financial model of the second chapter, we assume that the marketinterest rate satisfies Vasicek interest rate model, which is related to the underlying price process.In addition, we obtain the value formula of warrant bonds under a Markov-modulated jumpmodel. Moreover, we also give the numerical solution of the warrant bonds under a Markov-modulated jump model by using Monte Carlo simulation method.Chapter4We consider the pricing problem of convertible bond with credit risk. We assumethat the default intensity follows a mean-reverting model, and presents the pricing formula ofconvertible bonds with the credit risk under a Markov-modulated jump difusion model.Chapter5We make a conclusion of this article and consider the improvement direction.