Option Pricing Models Under Double Exponential Jump Diffusion Process

Option,as an important financial derivatives.is a hot of finance field.At the same time option pricing is one of the core contents of modern finance theory,attracting many specialists’attention.In1973,Fischer Black and Myron Scholcs proposed the famous Black-Scholes option pricing model,which is the basis of financial derivatives prieing.Blaek-Scholes model is built under ideal market hypothesis. However,realistic market is not ideal and includes many uncertain factors. Therefore,many specialists extended the model from different points.From the empirical study of the market,Black-Scholcs model has two faults:the volatility smile and the asymmetric lepokuric features.In order to explain the two features, many specialists proposed different models.In2002, Kou advanced the double exponential jump diffusion model,which explains the two features above.Furthermore, the model can give not only analytical formula of vanilla option but also analytical formula of some exotic options such as barrier option、lookback option etc.In this paper,we introduce the classical Black-Scholcs model, European option pricing and barrier option pricing under the double exponential jump diffusion process.Then, we obtain analytical pricing formula of the standard double-barrier option in terms of Laplace transform. At last,we discuss the pa-rameter sensitivity of the European call option.We study a warrant of domestic market and find the outcome is better than Black-Scholes model.