The Application Of Martingaltheory In The Pricing Of Convertible Bonds

Martingale theory is an important part of stochastic process. Martingale theory has become a very power tool for the study of stochastic process and probability theory. Nowadays, it has penetrated to other disciplines, particularly in the insurance, securities and other financial sector has the extremely widespread application. As is known to all, as a kind of financial derivative products,convertible bonds have some characteristics that common bond and common stock does not have. Therefore, the research on convertible bonds pricing has important significance for keeping a stabilized monetary market.This paper mainly discussed different cases when the underlying stock follows different models. Through the study of general martingale pricing formula of convertible bonds, we deduced the martingale pricing formulas when the underlying stocks pay continuous dividend and the stock prices obey generalized index of O-U process.This paper consists of five parts. The first part introduces the research status at home and abroad, subject background and significance. The second part summarizes the theoretical knowledge including preliminary knowledge of modern theory of probability, stochastic mathematical about Brown movement,?Ito integral and martingale theory and the martingale pricing principle as well as the definition, properties, characteristics and the due value of convertible bonds.The third part introduces the pricing formulas of the ordinary convertible bonds, in this case, the underlying stock price follows geometric Brown movement and the risk-free interest rate is constant. In the fourth part, we assumes that the underlying stocks pay continuous dividends and market risk-free interest rate is related to time t, under this condition, the martingale pricing method is used to derive the convertible bonds pricing formula. In the fifth part, we change the model of underlying stocks into generalized index of O- U process that is more accord with the actual market situation, under this condition, the martingale pricing method is used to derive the convertible bonds pricing formula.