Trigeminal tree pricing lookback option model.
|Course||Probability Theory and Mathematical Statistics|
|Keywords||Lookback option The trinomial tree method The modified trinomialtree method convergence optimal exercise boundary|
This paper studies the trinomial tree method and its modified method of Lookback options when the underlying asset in a market which follows a diffusion model. In the methods of pricing options, binomial tree method is a classical numerical method and discrete model, trinomial tree method is the extention of the binomial tree method, and is better than binomial tree method in accuracy and speed of calculation.Lookback options are path-dependent options whose payoffs depend on the maximum or the minimum of the underlying asset price during the life of the options. This paper makes a detailed analysis about trinomial tree method and its modified method for Lookback options in diffusion models. The trinomial tree method is a discrete model and numerical algorithm for option pricing, But trinomial tree models of the Lookback options involve two state variables because an additional path-dependent variable is introduced, and too much calculation is involved for the trinomial tree model making the method is not feasible. Cheuk et al. gave a one-state binomial tree model for lookback options in diffusion models, and this paper generalize the results in Cheuk et al. to the trinomial tree method so as to give the one-state trinomial model for Lookback options. Because the one-state binomial tree method of Cheuk et al. exists some inconsistency, so the speed of convergence is slow, Dai gave a modified binomial tree method to improve the efficiency of the algorithm. we take the results of Dai  to trinomial tree method and give a modified trinomial tree method, we talk about the convergence of the modified trinomial tree method as well as the optimal exercise boundary of the modified trinomial tree method for the American lookback options. Finally, we show the numerical simulations of European and American lookback options undering the binomial tree method and trinomial tree method.