关键词: 亚洲期权, 蒙特卡罗模拟, 控制变量法, 多元控制变量估计

Abstract: Asian options are such popular exotic options that the valuation, especially the valuation of arithmetic Asian options which are traded in the OTC markets, is a problem of not only theoretical research but also practical applications. However, pricing Asian options is not an easy job, its difficulty lies in no closed-form representation for the probability distribution of the variable, a sum of correlated lognormal random variables, which determines the option payoff at expiration. Under the risk-neutral framework, the price of Asian options is just the risk neutral expectation of discounted payoff. Monte Carlo simulation with variance reduction techniques is a useful approach to estimate this expectation. A new multiple control variate estimator for Asian options is proposed, which is shown by numerical results to have significant improvement over others especially when t he time to maturity is long and the volatility is large.

Key words: Asian options, Monte-Carlo simulation, control variate technique, multiple control variate estimator