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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?



Question 829  option, future, delta, gamma, theta, no explanation

Below are some statements about futures and European-style options on non-dividend paying stocks. Assume that the risk free rate is always positive. Which of these statements is NOT correct?



Question 830  option, delta, gamma, no explanation

Below are some statements about European-style options on non-dividend paying stocks. Assume that the risk free rate is always positive. Which of these statements is NOT correct?



Question 834  option, delta, theta, gamma, standard deviation, Black-Scholes-Merton option pricing, no explanation

Which of the following statements about an option (either a call or put) and its underlying stock is NOT correct?

European Call Option
on a non-dividend paying stock
Description Symbol Quantity
Spot price ($) ##S_0## 20
Strike price ($) ##K_T## 18
Risk free cont. comp. rate (pa) ##r## 0.05
Standard deviation of the stock's cont. comp. returns (pa) ##\sigma## 0.3
Option maturity (years) ##T## 1
Call option price ($) ##c_0## 3.939488
Delta ##\Delta = N[d_1]## 0.747891
##N[d_2]## ##N[d_2]## 0.643514
Gamma ##\Gamma## 0.053199
Theta ($/year) ##\Theta = \partial c / \partial T## -1.566433
 

 




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