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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?