wu1oohenry

在做一个作业，其中需要对有barrier 的 rainbow option 做 hedge， 无从下手，请达人赐教~

万分感谢~！

martingale

个人看法：
Dynamic hedging：可以求得这个带有barrier的rainbow option的Greeks，然后根据Delta, Gamma等用标的股票（这里是多个）short对冲；
Static hedging：如果只是barrier好办，组合里用标准call, put期权对冲Barrier，以up-out call为例，若没触及barrier，这个期权收益就为标准call；若触及barrier，这个期权收益为零，因此可以用一个标准call和另一个或数个call或者put期权组合来对冲barrier期权，其中另一个或数个call或者put期权的目的是构造一个收益，使得当股票价格为barrier值时它的收益为零。
考虑到了rainbow后我不知道static hedging应该怎么处理，知道的帮忙解释一下。

EnglandWhite

There are many different kinds of rainbow options, suppose you are talking about an option on the maximum or minimum stock return of a basket.

Delta hedging is a standard way. Each stock will have a delta which will be approximately equal to (plus or minus) its probability, under the risk-neutral distribution, of being the maximum (or minimum).

The problem for delta hedging is as time approaches zero you find delta of one stock approaching 1 (or -1) while the others approach zero. This is fine actually, but if there is a barrier, delta hedging breaks down because it will become so unstanble when underlying asset approaching barrier.

Aonther problem is the parameter of correlation matrix, it is so tricky that no one can asure you can get correct estimates. The best way I think is to find out similar products to backout implied correlation, and do some statistics to come up with a reasonable spread.

I agree with upstairs that static hedge with uncertain parameter is a solution to aforementioned problem(hard to explain details here, all in CQF). Static hedge with multiple underlying is no difficult than single underlying, simply including vanilla options with each underlying.

[ 本帖最后由 EnglandWhite 于 2008-2-1 03:18 AM 编辑 ]

QuantHR

would it be pissible to static hedge rainbow option? if yes, how to deal with max or min return in this case, thanks.

EnglandWhite

Yes, why not. I don't know much details about closed form solution, but it can be done numerically. It is not difficult to write the payoff function of Max or Min return on equity, once you define payoff function you can either use FD or MC to compute its price.

QuantHR

引用:

原帖由 EnglandWhite 于 2008-2-1 03:50 AM 发表
Yes, why not. I don't know much details about closed form solution, but it can be done numerically. It is not difficult to write the payoff function of Max or Min return on equity, once you define pay ...

是的，但你这个应该属于dynamic hedging。
如果static hedging应该只能有个上下限，无法精确hedging.