Let be random variable and let be measurable function such that with. Other methods include analytic method and finite difference approach. By the argument above, we know that. Step 1 sample path generation. In this part, we describe the numerical scheme of the computation of Asian arithmetic option Greeks with control variate method. Rogers and Shi solve the pricing problem with a PDE approach. It should also be noted that the discretization of the continuous process could introduce errors see Broadie et al.
As a consequence, we obtain an analytical formula for of Asian geometric average call option, which will be used as a control variate in the Monte Carlo simulation.
The Scientific World Journal
In the case of Asian option, the payoff of geometric Asian option is set to be a control variate in order to improve the effectiveness of the payoffs of algorithm Asian option prices. It got its name aroundwhen David Spaughton and Mark Standish worked for Bankers Trust in Tokyo, where they developed the first commercially used pricing formula for options linked to the average price of crude oil. The payoff of Asian arithmetic average call option with strike price is given by Since no analytical solution is known, a variety of numerical approximation techniques have been developed to analyze the Asian arithmetic average option. Let us first outline some general principle of Monte Carlo method and variance reduction techniques. See Boyle and Potapchik [ 11 ] for an extensive survey of relevant literature. In the path integral approach to option pricing the problem for geometric average can be solved via the Effective Classical potential  of Feynman and Kleinert. It is easily seen that the variance of is less than the crude Monte Carlo estimator.