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：

Part B

The change in the price of put options will be greater for an instantaneous decrease in the price of the underlying equity than for an instantaneous increase in the price of the underlying equity of equal size.

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. This can be addressed by adjusting the put option price for the effect of gamma, which is analogous to the convexity adjustment of a bond’s price.

我想

delta =（P1-P0)/(S1-S0)

  -1 <delta <0

因此，put options的价格变化小于股票价格的变化。由的定义即可知。

根据答案出题人想问的是：

根据由delta ，hedge 算出来的值与真实的股票价格的变化相比，谁大？