Discrete Arithmetic Average Asian Option Pricing Based On Double Non-Uniform Distribution Algorithm

Option refers to a contract,gives the holder the right to buy or sell an asset at a fixed price on or before a specific date,depending on the type of the option.With the increasing complexity of the financial market,traditional options can no longer satisfy the changes of customers’ demands.Therefore,along with standard options as European options and American options,there are many new trading varieties in the financial market in order to avoid risks.These new trading varieties are called "new options" or "exotic options".The biggest characteristic of new trading varieties is path dependence.In other words,the determinant of income is no longer the price of the underlying asset on the maturity date,but closely related to all floating paths of the underlying asset price during the option validity period.In especial,Asian option is one of the basic forms of exotic option.The main reason for the rapid development of Asian options is that the underlying asset price is considered to be less likely to be manipulated due to the path-dependent characteristic,so that can avoid market risks.Therefore,the cost of Asian options is relatively small.According to many current research results,their main target is continuous Asian options,but in fact,after in-depth market research,we can find that the most common Asian options in the current market are generally discrete monitoring arithmetic average Asian options.In order to keep pace with the development of domestic financial market and its demand,this paper mainly studies discrete arithmetic average Asian options as a main point.Firstly,I take the discrete arithmetic average Asian option as the research object,optimize the pricing algorithm on the binary tree model proposed by Hsu,and verify its feasibility.Then,the Gauss-Hermite quadrature algorithm is used to build a twodimensional grid model.Then,not only the nonuniform scheme is adopted for the distribution of the number of arithmetic averages,but also the geometric average distribution is used to nonuniformly distribute the arithmetic averages of each grid point,and the relevant assumptions are tested to formulate the optimal model.When determining the algorithm,this paper mainly takes the European fixed price Asian call option as the starting point.Compared with other different types of Asian options,we can also use this algorithm when setting the price.Finally,according to the data obtained from the research,it can be found that the accuracy of the option value algorithm through the double-layer non-uniform distribution scheme is much higher than that of the uniform distribution,which is very similar as the option value of the benchmark algorithm.Moreover,when our monitoring times are relatively large,the time efficiency of our algorithm is much higher than that of Hsu.