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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 ($) S0 10 10
Strike price ($) KT 12 7
Risk free cont. comp. rate (pa) r 0.05 0.05
Standard deviation of the stock's cont. comp. returns (pa) σ 0.4 0.4
Option maturity (years) T 1 1
Option price ($) p0 or c0 2.495350486 3.601466138
N[d1] c/S   0.888138405
N[d2] N[d2]   0.792946442
N[d1] p/S -0.552034778  
N[d2] N[d2] 0.207053558  
Gamma Γ=2c/S2 or 2p/S2 0.098885989 0.047577422
Theta Θ=c/T or p/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? All other things remaining equal:



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

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 ($) S0 20
Strike price ($) KT 18
Risk free cont. comp. rate (pa) r 0.05
Standard deviation of the stock's cont. comp. returns (pa) σ 0.3
Option maturity (years) T 1
Call option price ($) c0 3.939488
Delta Δ=N[d1] 0.747891
N[d2] N[d2] 0.643514
Gamma Γ 0.053199
Theta ($/year) Θ=c/T 1.566433