Pricing The Value Of Non-callable Convertible Bonds

Convertible bond is a converted financing implement between bonds and stocks and possess the characterizations of bonds and stocks.It offers bondholders the right of converting bonds in specific price to corresponding quantity of stocks in regulared periods.Convertible bonds play a specific and sinificant part in the development of capital markets in China.Our stock market is at the initial stage of development and market volatility is intensive.At this time,convertible bonds provide a kind of steady regulatory mechanism.When stock prices rise sharply,the continuous pressure of converting bonds to stocks,possessed by convertible bonds,will inhabit the soaring pricing.When stock prices slumped,convertible bonds can minimum the loss of investors.The pricing of convertible bonds is an essential problem in recent researches on convertible bonds.Reasonable pricing mechanism is important for both investors and issuers.There have been many research works on the pricing of convertible bonds both home and abroad.These research works relate to price modeling,numerical method,empirical study and etc.Specifically,there are two parts in price modeling, one of which is constructed models whose variables are based on company values. Another kind is Simple models based on stock prices.Numerical methods mainly focus on binary tree methods,Monte Carlo simulation methods and finite deference methods and etc.Ingersroll(1977)first applied option theory to the pricing work of convertible bond and provided the classical One-way model.With the assumption that convertible price is only based the company value V_t,Ingersoll attained a partial differential equation with an variance of the company value.Then the optimal convertible strategy for holders and the optimal call policy for issuers.Based on Ingersroll's work,Brennan and Schwartz(1977) considered pricing a convertible bond in the firm's value framework for more general cases such as the payoff of stock interests.Moreover,A finite difference scheme was introduced to solve the pricing Partial Differential Equation.Brennan and Schwartz(1980) extend their pricing method by including stochastic interest rates.His work is made under the assumption that convertible bond prices are influenced not only by the company value but also the interest rates.Currently convertible bond pricing models all make the values of company stocks as variances because the value of company is difficult to predict.This method is called Simple method.The most insignificant models are McConnell & Schwartz(1986) model and Tsiverioti & Fernandes(1998) model.The Analysis framework of Simple Model is similar to Structure Model.Under the assumption that the market is perfect, we obtain the partial differential equation of convertible bonds by the method of no-arbitrage principle,and then construct the edge condition which is satisfied by convertible bonds.At last,the numerical solutions are got by numerical methods.In this paper,innovation is:1:We would like to provide a more comprehensive and thorough analysis of the noncallable convertible bonds.Our analysis framework relies on the reflected Backward Stochastic Differential equation approach.We characterize the value functions of the noncallable bonds in terms of the reflected Backward Stochastic Differential equation,Then the relationship between the value function of convertible bonds and reflected backward stochastic differential equations with single reflect(RBSDE) is built at the same time,and provide the optimal conversion strategy for bondholders.2:We get the value of non-callable convertible bonds by numerical methods.So far, Many studies on pricing the convertible bond with LSM(Least Square Monte Carlo simulation method)have been based on the Geometry Brown Movement Model for simulating the paths of stock price.Comparing the GARCH model with the Geometry Brown Movement Model in constant fluctuating rate,we found the results of empirical studies have proved the former better to accord with the factual for capturing the path of the stock price.Therefore,The former has been adopted in our numerical simulation.Then we provide the optimal convertible strategy.The simulating results are lower than the factual values.This is caused by the shortcomes of the simulation method.