[讨论]关于亚式期权估价的mc方法

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请问在使用monte carlo方法对亚式期权估价时为什么不能用对偶变量技术？

我觉得对偶变量也能加速收敛方差，

而控制变量法可用于亚式期权估价？两者关键区别在哪里？

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关键词：亚式期权 Monte Carlo Carlo 控制变量 mont 讨论 期权

没有人研究这方面的吗？

以下是引用jack9910在2006-5-22 22:40:00的发言：

请问在使用monte carlo方法对亚式期权估价时为什么不能用对偶变量技术？

我觉得对偶变量也能加速收敛方差，

而控制变量法可用于亚式期权估价？两者关键区别在哪里？

Of course you can use antithetic variables. Why not?

Geometric Asian is usually used as a control variate for arithmetic Asian.

但用对偶变量技术要求payoff是随机抽样样本的单调函数，

但亚式期权好像又是不能满足这个条件

以下是引用jack9910在2006-5-24 23:32:00的发言：

但用对偶变量技术要求payoff是随机抽样样本的单调函数，

但亚式期权好像又是不能满足这个条件

Suppose we want to calculate the expectation of f using Monte Carlo and z is a standard normal variate.

Antithetic variables can reduce variance if Cov[f(z), f(-z)] < 0. This always true if f is monotonic in z. However, f does not have to be monotonic in z to make the covariance negative. For a complicated function like the Asian option payoff, it is diffcult to show the covariance is negative. But it is equally difficult to show it is negative. So why not still using antithetic variables and hopefully the covariance is negative.

The rule of thumb is that, if you are using pseudo-random numbers, and the expection only involves low momemts, then antithetic variables should always be used, because they are so easy to use. In the worst case, your variance is not reduced, but there is no harm using them. However, do not use antithetic variables if you are using quasi-random numbers.

我也想知道

以下是引用jory1002003在2007-4-4 18:48:00的发言：
我也想知道

计量matlab那里我发过一个，你自己搜一下吧