| Financial time series are often change due to changes in economic policy or the occurrence of major social events. Obviously,when the structure changes, the traditional process of diffusion can not be a good fit to the financial data model, such as stock prices, interest rates. For this reason, many scholars have introduced models with jumps. Rydberg-Shaphard noticed in the actual market price movements is a discrete process, so that he proposed to give up the Black-Scholes model which used continuous geometric Brownian motion to describe the underlying asset price movements, in stead to use a pure jump process to describe the price process. Like all models with jumps, the market under pure jump model is also incomplete market. In incomplete markets, contingent claims generally can not be fully replicated, and the set of equivalent martingale measure is usually not a single point set. In this paper, a two-dimensional pure jump model is used to study the outside barrier option pricing problem. A minimum entropy martingale measure is picked from the set of equivalent martingale measure as a pricing measure, and we calculate the minimum entropy equivalent probability measure of outside barrier option under two-dimensional pure jump model. The no-arbitrage constraints are embedded in the outside barrier option pricing problem, and we have a nonparametric pricing method based on the two-dimensional model. This method only needs historical data to calculate the state space of jumps size of the barrier process and stock price process, and no need of estimate of the volatility. So that we solve the difficulties inherent in the calculation due to the complexity of the outside barrier options,and we investigate the effectiveness of the non-parametric method through simulation. |
