The Simulation And Optimization Of Asian Options Pricing

Options as stock derivatives, the pricing problems have been the focus ofacademia. The standard European options have explicit analytic solution, butthey can no longer meet the increasing market demand; So, the market emergemany new options.these new options are mostly related to the path of theunderlying asset price movement, also known as path-dependent options.Asian options are typical strongly path-dependent options, depend on theunderlying asset price of average in the validity; The adoption of the averagereduces the price volatility, makes the Asian option premium is lower than theother options and is welcomed by the market. However, the Asian optionpricing problem is still not fully resolved, when the average is the arithmeticmean, can not give analytical solution. Now the use of numerical algorithmsfor its valuation is more popular.This paper introduces the meaning of the options, the types of options,the B-S model and the common numerical methods first. Secondly, this paperintroduces Asian option， Asian option pricing and Monte Carlo simulation;However, geometric average Asian options have analytical solution while thearithmetic average Asian options are no analytical solution. Finally, this paperfocus on the arithmetic average Asian option pricing simulation and processsimulation; The use of methods are the Monte Carlo simulation and thequasi-Monte Carlo simulation. In this section, the first is to analyze thepseudo-random sequences and the quasi-random sequence, give the statisticalcharacteristics of the sequences, and compare them; And then the use ofdifferent sequence of random numbers and different variance reduction for thestandard European option pricing simulations is to compare differentsequences and different ways; Finally, to simulate the Asian option pricing,and compare European option, give the relevant conclusions.The results show that: For low-dimensional problems, thepseudo-random sequence assembled slower; The introduction of variance re-duction techniques can accelerated the convergence and reduced the volatility of the simulation; the use of quasi-random sequence of quasi-Monte Carlosimulation resulted better and assembled faster; The control variable techniquehad more advantages than the dual variable technology. And forhigh-dimensional problems, quasi-random sequence did not show more ad-vantages than the pseudo-random sequence, even worse than the effect ofpseudo-random sequence; The effect of control variables technique was alsovery weak. The reasons for the quasi-random sequence is prone tohigh-dimensional highly correlated, halton sequences began clustering of12dimensions, sobol sequence began clustering of more than200dimensional.Under normal circumstances, if the dimension of the problem is less than10dimensions, the use of quasi-random sequence is better, especially the haltonsequence, and above the20-dimensional, the use of sobol sequences orpseudo-random sequence is better.