Strategies Under The Framework Of The Jump Diffusion Model Stock Trading And Binary Tree

This paper studies stock trading strategy and binomial tree methods when the underlying asset in a market which follows a jump diffusion model. Different with the traditional diffusion model, the jump diffusion models assume that the price of underlying asset is influenced by the Brownian motion and Poisson process at the same time. This model can give a fine explanation to sudden changes in the market, so it is more reasonable than the diffusion model.For some reason, an investor holding a stock needs to sell the stock over a given investment horizon. When is the best time for him to sell it? Obviously, everyone hope to sell the stock at the maximum price over the entire horizon, which is however impossible to achieve. We use the optimal stopping theory to study the trading strategies which could achieve the maximum of the selling price comparing to the aforementioned maximum price under some utility functions. With the assumption that the stock price follows a jump-diffusion model, we give the criteria for measuring the quality of the stock when logarithmic function and linear function are taken as the utility functions. We verify that the optimal strategy is to hold on to the stock selling only at the end of the horizon for "good stock" and to sell the stock immediately for "bad stock".The binomial tree method(BTM) is one of the most popular appoaches to pricing options.After that it is extended by Kwang Ik Kim,et al.[1]to jump-diffusion models.But the methods that they proposed is not consistent with the continuous model.In this paper,we propose a modified binomial tree method which is consistent with the continuous from the view of PDE.And we also prove the convergence of the optimal exercise boundary in the binomial tree approximation to Amercian lookback options and prove some properties of the modified binomial tree method.