Asian Option Pricing Model Trigeminal Tree

In this paper, we study the trinomial tree method for pricing Asian options and its related properties when the underlying asset in a financial market which follows the diffusion model. In the theory of pricing options, the binomial tree method is a classical numerical way and discrete model, while the trinomial tree method is extended to the binomial tree method, its on the computing precision and computing speed are better than the binomial tree method.Asian options are strong path-dependent related options whose payoffs depend not only on the underlying asset prices but also on the average of the underlying asset prices for the throughout the period of validity. In the paper, employing Jiang[1] and others research methods about the binomial tree methods for Asian options in diffusion models, we get the trinomial tree method for pricing Asian options and equivalence of one-state explicit difference scheme, and under the theoretical framework on the notion of viscosity solution,we prove the consistency of the trinomial tree for American-style Asian options. Asian options ordinary binomial tree method due to the introduction of the path variable as a double state variable model, making the computation is lager, it usually cannot be applied to the real financial field, while the trinomial tree method for Asian options have the same problem. Cheuk[2] and others by using the method of variational simplification get another strong path-dependent in the diffusion model of one-state variable binomial models for look back options, and Dai [3] using the similar idea got the one-state variable binomial tree models for geometric Asian options, which makes real calculation is feasible. In this paper,we push the Dai’s[3] results to the trinomial tree method models, which gives the one-state variable trinomial tree method for European/American-style fixed/floating strike geometric Asian option with the continuously sampled observations and discretely sampled observations, and proves their equivalence of the explicit difference scheme.