Option Pricing And Empricial Studies Based On Double Exponential Jump Diffusion Model

Chinese financial market is experiencing prosperities and innovations at an unprecedented speed, among them is a wider product range of financial derivatives. The lunch of Shanghai Composite 50 ETF marks Chinese financial derivatives market has entered a fast-developing era. A closer scrutinization, however, reveals investor’s further requirements, either hedging their positions in the spot market or speculation.Since F. Black, M. Scholes and R. Merton has made their fundamental achievements in option pricing theory, Financial Mathematics, as an emerging field of study, has experienced rapid growth, in both theory and application. Recent occurrence of black swan events in the market and many problems raised in financial reforms, prompt us to rethink whether Black-Scholes Model, which is established on assumption of Brownian Motion and normal distribution, is still valid in the present. In 1976, for the first time Merton established the jump-diffusion model of underlying asset, meanwhile he studied corresponding option pricing problem under the normality assumption of unsystematic jump risk. After Merton’s breaking-through contribution in theory, following him many scholars has further studied this area and then proposed many extensions.Balck-Scholes-Merton Model has been widely accepted and adopted in the financial market, yet recent study suggest it failed to describe volatility of underlying asset within a reasonable range of error. The major errors are:(1) Some important economic phenomenon lies behind the jumps of underlying asset in the capital markets; (2) The returns distribution of assets can possibly be asymmetric and with fat tails.In 2002, Steven Kou proposed a double exponential jump diffusion mode. It can generate a high peak fat tail distribution. More importantly, this model can closed pricing formula for European and Exotic Options. Based on these features, double exponential jump-diffusion model has been widely acknowledged.This paper discusses the founding basis and analytical solution of Kou’s model, and analyzes the impact of parameters in determining option price in the model. Shanghai Composite 50ETF is selected as an investigation subject, to access the advantages of Kou’s model. Finally, some forward looking suggestions to policy maker will be made by gauging market data and investment requirement.