550_446_2010 TA 02 - 550.446 Risk Management Analysis and...

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550.446 Risk Management Analysis and Hedging, Spring 2010 TA Section 02 Peter C.L. Lin peter.lin@jhu.edu 1 Homework Review 4.16 The investors overall return is 1 . 08 × 0 . 92 × 1 . 12 × 0 . 88 - 1 = - 0 . 0207 or - 2 . 07% for the four years. 6.16 The price, delta, gamma, vega, theta, and rho of the option are 3 . 7008, 0 . 6274, 0 . 05, 0 . 1135, - 0 . 00596, and 0 . 1512. When the stock price increases to 30 . 1, the option price increases to 3 . 7638. The change in the option price is 3 . 7638 - 3 . 7008 = 0 . 063. Delta predicts a change in the option price of 0 . 6274 × 0 . 1 = 0 . 0627 which is very close. When the stock price increases to 30 . 1, delta increases to 0 . 6324. The size of the increase in delta is 0 . 6324 - 0 . 6274 = 0 . 005. Gamma predicts an increase of 0 . 05 × 0 . 1 = 0 . 005 which is (to three decimal places) the same. When the volatility increases from 25% to 26%, the option price increases by 0 . 1136 from 3 . 7008 to 3 . 8144. This is consistent with the vega value of 0 . 1135. When the time to maturity
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550_446_2010 TA 02 - 550.446 Risk Management Analysis and...

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