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Option Sensitivities and Option Hedging

Answers to Questions and Problems
1. Consider Call A, with: X $70; r 0.06; T t 90 days; DELTA, GAMMA, THETA, VEGA, and RHO for this call. c DELTA GAMMA THETA VEGA RHO $1.82 .2735 .0279 8.9173 9.9144 3.5985 0.4; and S $60. Compute the price, 0.4; and S $60. Compute the price,

2. Consider Put A, with: X $70; r 0.06; T t 90 days; DELTA, GAMMA, THETA, VEGA, and RHO for this put. p DELTA GAMMA THETA VEGA RHO $10.79 .7265 .0279 4.7790 9.9144 13.4083

3. Consider a straddle comprised of Call A and Put A. Compute the price, DELTA, GAMMA, THETA, VEGA, and RHO for this straddle. price DELTA GAMMA THETA VEGA RHO c p $12.61 0.2735 0.7265 0.4530 0.0279 0.0279 0.0558 8.9173 4.47790 13.6963 9.9144 9.9144 19.8288 3.5985 13.4083 9.8098

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CHAPTER 14

OPTION SENSITIVITIES AND OPTION HEDGING

4. Consider Call A. Assuming the current stock price is $60, create a DELTA-neutral portfolio consisting of a short position of one call and the necessary number of shares. What is the value of this portfolio for a sudden change in the stock price to $55 or $65? As we saw for this call, DELTA 0.2735 shares 1 call, costs: 0.2735. The DELTA-neutral portfolio, given a short call component, is .2735 ($60) $1.82 $14.59

If the stock price goes to $55, the call price is $.77, and the portfolio will be worth: .2735 ($55) $.77 $14.27

With a stock price of $65, the call is worth $3.55, and the portfolio value is: .2735 ($65) $3.55 $14.23

Notice that the portfolio values are lower for both stock prices of $55 and $65, reflecting the negative GAMMA of the portfolio. 5. Consider Call A and Put A from above. Assume that you create a portfolio that is short one call and long one put. What is the DELTA of this portfolio? Can you find the DELTA without computing? Explain. Assume that a share of stock is added to the short call/long

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