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Pat and Chris are both short 200 six month call options with a strike price of 75 on Noble Energy. Pat's position has been delta

Pat and Chris are both short 200 six month call options with a strike price of 75 on Noble Energy. Pat's position has been delta hedged while Chris' has been delta-gamma hedged. (Chris has access to a six month put option at 72.) The price of Noble is 77, the stock has an annual standard deviation of 28 percent, and the interest rate is 3 percent.


A: How much money will Pat and Chris make or lose if the price of Noble jumps to 91?


B: How much money will Pat and Chris make if the price of Noble falls to 64?

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