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# Determining Prices of Call and Put Options

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A stock has a spot price of \$35. Its May options are about to expire. One of its puts is worth \$5 and one of its calls is worth \$5. The exercise price of the put must be ___A__ and the exercise price of the call must be ___B__. (please show work for A & B)

#### Solution Summary

This solution determines the steps to determine the exercise prices of call and put options in the given case.

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## Q1: Use Derivagem to calculate the implied volatility of the call option. Q2: Use put-call parity to estimate the no arbitrage price of a March 100 put. Q3: Given the price determined in Q2, use Derivagem to calculate the implied volatility of the put option. Q4: What do you conclude about put-call parity and implied volatility for European options?

AD 13: The Dow Jones Industrial Average on December 22, 2009 was 10,464 and the price of the March 100 call was \$5.00. Assume the risk-free rate is 3.2%, the dividend yield is 2% and the option expires on February 20, 2010. (Note that the options are on the Dow Jones Index divided by 100.)

Q1: Use Derivagem to calculate the implied volatility of the call option.

Q2: Use put-call parity to estimate the no arbitrage price of a March 100 put.
Q3: Given the price determined in Q2, use Derivagem to calculate the implied volatility of the put option.
Q4: What do you conclude about put-call parity and implied volatility for European options?

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