**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 |
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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:

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 |
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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 |