The Empirical Study Of Double Exponential Jump-Diffusion Model In China

BSM model (Black-Scholes-Merton option pricing model) is the classical benchmark in option pricing. It has a great difference from the former option pricing formulas—it depends only on the observational variables or the estimable variables. They are all objective variables, not the subjective variables. So BSM formula avoids the dependence of the risk preferences of the investors.But in the past decades,there have been great challenges to BSM pricing model.The main problem comes from its unpractical hypotheses,all highly idealized,which make the model different from the reality of the market.From the empricial study of the market,two phenomena have attracted great attention: (1) the asymmetric sharp peak,and fat tailsf; (2) the volitility smile.Thus,in the past decades,a variety of development have been made to relax the hypotheses of BSM pricing model,in order to explain the sharp peak phenomenon and the phenomenon of volitility smile.One of the most important developments is the introduction of jump into the diffusion process in BSM pricing model so as to describe the stochastic process followed by underlying assets.But one of the major flaw of these models is that it is impossible to get an analytical solution for options and it is still harder to give analytical solutions for path-dependent options and interest-rate options.Kou (2002) advanced the double exponential jump diffusion model which is a simple model for assets with jump diffusion feature. Compared to the hypothesis of normal distribution with the same mean value and variance, the double exponential jump diffusion model has a higher peak and two heavier tails ; moreover ,it can describe the option "volatility smile" fairly well. It offers not only analytical solutions for both call options and put options, but also analytical solutions for barrier options, lookback options and interest options.This paper introduces the basic content of double exponential jump diffusion model,discusses its feature and applications,explores approaches to apply the model to reality,including parameters estimation and numerical approaches;it also proves the simplicity and feasibility of KDJ model and discusses the praticalbility and rationality of its application in option pricing in China;in the end,we use the model to price the only two types of options:warrants and convertible bonds and then compare it to the results of BSM pricing model.