Pricing Chooser Options Under Jump-Diffusion Model

With the evolution of economic globalization,financial derivatives have developed rapidly.As an important tool of risk management,option plays a decisive role in the financial market.The chooser option can reduce the cost and the risk of the investment comparing with the standard option,so it is important to price the chooser option reasonably.The key factor affecting the price of the option is the stochastic process followed by the price process of the underlying asset.Empirical research shows that the jump-diffusion process is more suitable for the actual situation than geometric Brownian motion.Therefore in this paper,we price the chooser option under the jump-diffusion model and the main contents are as follows:Firstly,we assume that the price process of the underlying asset follows exponential Lévy jump-diffusion process under the actual probability measure .We first construct a risk-neutral measure Q by mean-correcting.And then using measure transformation and the relationship between the characteristic function and the distribution function,we obtain the pricing formula of the chooser option.After that,we collect the historical data of Shanghai 50 ETF to estimate the parameters in the model using the moment estimation,and we perform numerical simulation.At the end,we discuss the effects of maturity date,choice date and strike price on the price of the option.Secondly,we assume that the price process of the underlying asset follows the jumpdiffusion process with time-varying parameters and the price process of the discount bond follows the geometric Brownian motion under the risk-neutral measure Q.And then we transform the expectation of the terminal payoff into the probability by constructing an appropriate probability measure and obtain the pricing formula of the option expressed in the integral form of the characteristic function by the help of the relationship between characteristic function and distribution function.Moreover we consider the sensitivity of the price of the option with respect to the parameters.