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?