The Research On Convertible Bond Pricing

Convertible bond is a special commodity on the securities market.The enterprise certainly appeal for direct financing from capital market due to it's unique nature.Convertible bond is a kind of both long-term debt and options of mixed financial tool.The convertible bond investment for investors can obtain the desired "good" effect.Therefore,how to accurately assess the value of convertible bonds is particularly important for investors and enterprises.This paper did some system research of convertible bonds pricing problems.Considering the impact on price volatility of stock prices,interest rates,asset value,etc,we establish models which are in accordance with the actual financial market.By using the actuarial method,martingale pricing,measure transformation and martingale pricing and FFT method,respectively in different complex degree of convertible bonds and the pricing formulas of the inference are givened.1.Discussing convertible bonds with default risk pricing problem.We consider the influence on the pricing of stock price and interest rate two-factor model.Firstly,according to a large number of empirical studies have found that the price of the stock with the long-range correlation and self-similarity,and the geometric fractional Brownian motion in accordance with these two properties,therefore,we use geometric fractional Brownian motion to depict the motion process of the underlying stock price,which more close to the actual financial market.Surely,the dividend distribution also be considered.Secondly,most of the literature is stochastic interest rate or interest rates.But this paper uses Hull-White rate model to depict the interest rate movement.Mainly because the Hull-White rate model has the characteristics of mean reversion characteristic,and Vasicek model and CIR model can be extended from it.And KMV model is used to describe the existence risk of default in this part.Lastly,we use actuarial pricing to solve pricing problem and convertible bonds pricing with default risk formula is givend.2.Mainly taken additional convertible bond redemption terms into consideration.We use jump diffusion model to depict the stock price and interest rate with the Vasicek model.We obtains the attached redemption clauses of convertible bonds pricing formula by using the transformation of clever and martingale methods.Then we gives the ordinary pricing formulas of the convertible bonds.3..We analyze the attached back to sale terms of convertible bonds pricing problem.Bying the martingale method and measure transformation methods,the attached back to terms convertible bonds pricing formula is givened when the stock is subject to jump diffusion,interest rates is stochastic interest rate and transaction costs is in the case.4.Discussing the stochastic volatility and double exponential jump diffusion model under stochastic interest rate of the detachable convertible bonds pricing.Its characteristic is that:firstly,the emperiment data shows that the double exponential jump diffusion model fitting stock data is better than general jump diffusion model and double exponential jump diffusion model can overcome the traditional Black-Scholes model when exsists stock distribution of peak characteristics and volatility smile.Double exponential jump diffusion can be used for heavy(tail)and the excessive reaction(peak)model.Secondly,the volatility is stochastic and volatility is calculated by a mean reversion process.Lastly,we use a new pricing method of FFT method for the separation of trading convertible bonds pricing.