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Question 793  option, hedging, delta hedging, gamma hedging, gamma, Black-Scholes-Merton option pricing

A bank buys 1000 European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.

European Options on a Non-dividend Paying Stock
Description Symbol Put Values Call Values
Spot price ($) ##S_0## 10 10
Strike price ($) ##K_T## 12 7
Risk free cont. comp. rate (pa) ##r## 0.05 0.05
Standard deviation of the stock's cont. comp. returns (pa) ##\sigma## 0.4 0.4
Option maturity (years) ##T## 1 1
Option price ($) ##p_0## or ##c_0## 2.495350486 3.601466138
##N[d_1]## ##\partial c/\partial S##   0.888138405
##N[d_2]## ##N[d_2]##   0.792946442
##-N[-d_1]## ##\partial p/\partial S## -0.552034778  
##N[-d_2]## ##N[-d_2]## 0.207053558  
Gamma ##\Gamma = \partial^2 c/\partial S^2## or ##\partial^2 p/\partial S^2## 0.098885989 0.047577422
Theta ##\Theta = \partial c/\partial T## or ##\partial p/\partial T## 0.348152078 0.672379961
 

 

Which of the following statements is NOT correct?




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