The Price Of The European-Style Arithmetic Average Asian Option Research

Evading risk in financial trading market cries for pricing options to a nicety .Asian option,as the most flourish options in the finace market ,the pricing has been focused on always.The exact pricing formula for the geometric average Asian option had existed,but as to the European-style arithmetic average Asian option,due to the dependence structure between the prices of the underlying asset,no analytical formula exists.On the hypothesis that the market is frictionless and without transaction costs,on the base of B-S's and in the binomial tree model,we provide several algorithms for computing an accurate value of the European-style arithmetic average Asian option.Following Rogers and Shi and by Jensen's inequality,many different upper and lower bounds are provided;meanwhile a formula have got by the comonotonicity and approximating the distribution function.All of the algorithms are easy for programming.With the development of computer,more accurater price can be computed quickly.And numerical example proved that these algorithms are very accurate.Inspired by the binomial tree model,We also provide the algorithms under the multiplicative triple tree model.And the convergence is provided.We also show an algorithms to compute the American style arithmetic Asian option in section 4.At last ,an example is provided to show the asian option's application.