The arithmetic Half-Asian option is a generalized Asian option with no analytic pricing formula. In practice, simulation algorithms such as Monte Carlo method is mostly used in option pricing. Although the pricing accuracy is high, the calculation time for pricing is long. A fast algorithm for pricing the arithmetic Half-Asian option named the semi-analytic method is obtained by combining the improved Monte Carlo method and moment approximation method, which greatly reduces the computation time for pricing under the premise of ensuring accuracy. Then, the semi-analytic method is improved by using antithetic variable technique to further reduce the computation time for pricing.
