| Today with the rapid development of global financial markets and the emergence of the large number of financial products, derivatives was welcomed by more and more investors . In today's international financial markets in addition to the transaction of European, American and other standard options, it also emerged lots of other unstandard options ,they were changed or combinated by standard options. For example Asian option . Asian Options as one of the most active options ,its pricing has been widespread concerned. For geometric average Asian options it is easy to get the analytic pricing formula . But to the arithmetic average Asian options, because of the path depended that we can not get the analytic pricing formula. So people try to use Monte Carlo method to price it.It's useful to price them using Monte Carlo simulation. But there is big variance.In order to reduce variance, researchers give out Quasi-Monte Carlo and many useful reduce variance techniques, control variate method is a very important method in pricing Asian option.We must choice different control variates and random sequenes for different options, so how to choice the control variate and random sequenes is a important problem. In this paper ,we discuss the pricing of arithmetic average Asian options using control variate Monte Carlo simulation, based on the B-S model.And we compare different control variates to choice the better control variate and better random sequenes.This paper contains two main research works:The first one is to introduct the methods of generation Halton,Faure and Sobol sequenes.Advantages and disadvantages of each sequenes are stated on independent computational experiments by author. The second one we give the general step of control variate Quasi-Monte Carlo simulation for pricing the arithmetic average Asian options,and give out one new control variate: sum control variate. And we make a numerical analysis on the simulation result with different control variates in detail. |
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