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eee · 2019年02月13日

关于2012年真题涉及gamma的问题

题干:

The bank’s risk manager wants to understand the sensitivity of the price of the put options that have been sold. Delport explains that traders frequently use option deltas to estimate the sensitivity of options to changes in the price of the underlying equity. However, actual option price changes will differ.
B. Determine whether the change in the price of the put option will be greater for an increase or decrease in the price of the underlying equity. Justify your response with one reason.
Note: Assume the increase and decrease are immediate and of equal value.


答案:

For put options, the delta will underestimate the price effect of decreases in the underlying equity and will overestimate the price effect of increases in the underlying equity. This is due to the convex relationship between put option prices and the price of the underlying equity


这个点我记得主要是在一二级讲解债券和利率关系的时候讲到,利率降低债券价格升高的幅度大于利率升高债券价格下降的幅度,而put option答案里面涉及overestimate the price effect of increase in the underlying,这个overestimate我不太理解,现在三级好像没涉及有点淡忘了,可否以图形形式解答一下,谢谢。

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已采纳答案

竹子 · 2019年02月14日

gamma的影响类似于债券中的convexity,即涨多跌少。由于股票价格上升,put option 价格下降,但实际下降的金额小于delta计算出来的金额(跌少),所以delta会高估价格下降的金额,比如实际下降了2块,但delta估计下降的是2.5块。图形如下:

delta是一个直线,根据delta的影响,如果价格变化△S,那么put option价格变化应该是绿色部分。

但实际上,是一条曲线,实际的价格变化应该是橙色部分。

所以delta 高估了价格的下降量。

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