亚洲期权价格的一个新的多元控制变量估计

A New Multiple Control Variate Estimator for Asian Options

提出了一个新的用来估计亚洲期权价格的多元控制变量估计 ,由数值结果可知 ,当离到期时间很长或标的资产收益的波动率很大的时候它对其他控制变量估计有显著的改进。

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 the time to maturity is long and the volatility is large.