Convertible Bonds Pricing With Term Structure Of Interest Rates Based On Variance Gamma Model

As a financial derivative product, convertible bond concurrently has characteristics of share and debt. Convertible bond pricing models, usually assume that the underlying asset follows geometric Brownian motion. However, more and more researchers argue that, the price of financial assets in actual market is discontinuities and non-normality. Therefore, more and more researchers describe the actual return of price with jumps and stochastic processes.There are mainly two types of models:jump-diffusion model and infinite activity pure jump model. Particularly, by introducing more parameters skewness θ and kurtosis v. Variance Gamma (VG) model could depict some economical phenomena better. VG process is a finite variation process with high skewness and fat tail. Also, Classic Black-Scholes option pricing model suffers the problem of volatility smile, while assuming underlying assets logarithmic price follows VG distribution can overcome this problem.To price convertible bond, this paper assumes that asset logarithmic price follows variance gamma process. Deduced from term structure of interest rate curve, the same term of interest rate of national bonds was used as risk-free rate. We analyzed the effects of call item and put item, and deduced the optimal execution strategy of convertible bonds. The least squares Monte Carlo simulation was used to price convertible bond. Empirical analysis of Sinopec convertible bond shows that the variance gamma model theoretical price and the actual price are in good agreement. Compared with the BS model, pricing results also shows that the variance gamma model has smaller error.