s****y
发帖数: 109 | 1 How to capture free boundary of a American Option by the least square
simulation? My solution is to solve the equation "Exercising Value =
Continuing Value" where the Exercising Value EV(S)=S-K; Continuing Value CV(
S)=a+b*S+c*S^2, where the coefficient a, b, c is estimated by least square
regression (suppose the base function is polynomial). Is this correct?
Thanks a lot. | h*y
发帖数: 1289 | 2 严格的说Cont. Value=a+b*S+c*S^2 + Error
所以需要解的方程应该是Exercise Value=a+b*S+c*S^2 + Error
通过解Exercise Value=a+b*S+c*S^2得到的exercise boundary往往非常zigzag，因为在
每个时间点上的regression结果都不一样，error的差别也可能很大。
CV(
【在 s****y 的大作中提到】
: How to capture free boundary of a American Option by the least square
: simulation? My solution is to solve the equation "Exercising Value =
: Continuing Value" where the Exercising Value EV(S)=S-K; Continuing Value CV(
: S)=a+b*S+c*S^2, where the coefficient a, b, c is estimated by least square
: regression (suppose the base function is polynomial). Is this correct?
: Thanks a lot.
| s****y
发帖数: 109 | 3
为在
十分感谢, 解决了很多疑问！但是不知如何估计error? 有什么方法可以减小error：通
过变换base function? 另外，如果polynomial function作为base function是否有可
能存在方程无解？该如何处理呢？
【在 h*y 的大作中提到】
: 严格的说Cont. Value=a+b*S+c*S^2 + Error
: 所以需要解的方程应该是Exercise Value=a+b*S+c*S^2 + Error
: 通过解Exercise Value=a+b*S+c*S^2得到的exercise boundary往往非常zigzag，因为在
: 每个时间点上的regression结果都不一样，error的差别也可能很大。
:
: CV(
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