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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? 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 ($)	$S_0$	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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