Lecture_19

Lecture_19 - Options and Derivatives Professor Ruslan...

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Professor Ruslan Goyenko Options and Derivatives 1
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Put-Call Parity Where does the put-call parity come from? Consider two portfolios: Portfolio A: One European call option plus an amount of cash equal to Present Value of X Portfolio B: One European put option plus one share. Call + P.V. of Exercise Price = Put + Security Price If these two portfolios produce the same pay-offs under all states of nature, then they should have the same price. 2
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Put-Call Parity Portfolio Bad State of Nature X>S Good State of Nature S>X A a. Call not exercised; b. Cash ($X) Hold: Cash ($X) a. Call exercised; b. Get share; c. Pay with $X Hold: Share (S) B a. Exercise put; b. Get strike price ($X) Hold: ($X) a. Put not exercised; b. Remain with share Hold: Share (S) 3
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Put-Call Parity: An Example If the Put-Call Parity does not hold, then arbitrage opportunities will arise. Example: Suppose that the security price is $31, the exercise price is $30, the risk-free rate is 10% per annum, the price of a 3-month European call option is $3, and the price of a 3-month European put option is $2.25. Do we have mispricing? If yes, could we make arbitrage profits? 4
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Example Value of Portfolio A: Value of Portfolio B: Portfolio B is overpriced relative to portfolio A. What is the arbitrage strategy? Buy securities in Portfolio A and short the securities in Portfolio B. 5
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Lecture_19 - Options and Derivatives Professor Ruslan...

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