求问期权交易策略的理论证明

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从理论上讲，期权策略组合（股票、期权通过种类、买卖方向、执行价格、期限不同等的组合）可以复制任意的收益形态，请问这个理论上可以证明吗，或者说曾经是否已有论文里证明了这个结论（我貌似记得有论文已经证明了），谢谢啦！

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关键词：交易策略 期权交易 可以复制 期权交易

Can't remember which paper, but I give a rough proof.
hope help.

Chemist_MZ 发表于 2014-1-13 14:05
Can't remember which paper, but I give a rough proof.
hope help.

万分感谢哈！但要是有原来的paper就好了，呵呵，再次感谢

Chemist_MZ 发表于 2014-1-13 14:05
Can't remember which paper, but I give a rough proof.
hope help.

Very nice proof.

One more note: not all payoffs are smoothing. However, certain smoothing technique can be employed. See also Chapter 23 of the book <Interest Rate Modeling> by Andersen and Piterbarg. With a smoothed payoff, the above proof is then applied.

Carr, P. & Picron, J. (1999), `Static hedging of timing risk.',Journal of Derivatives pp. 57-69

yuangord 发表于 2014-1-14 00:03
One more note: not all payoffs are smoothing. However, certain smoothing technique can be employed.  ...

thanks very much,

I know a basic method is to use some piecewise smooth function fn(x) to approximate f(x). As n goes to infinity, fn(x) will converge to f(x) which is a non-smooth payoff (e.g. with kinks)

幻影斩 发表于 2014-1-14 09:16
Carr, P. & Picron, J. (1999), `Static hedging of timing risk.',Journal of Derivatives pp. 57-69

Thanks very much, the paper is by Carr in my memory. Just can't remember the paper's name :-)

幻影斩 发表于 2014-1-14 09:16
Carr, P. & Picron, J. (1999), `Static hedging of timing risk.',Journal of Derivatives pp. 57-69

万分感谢哈