DM3-Put-Call Parity

# DM3-Put-Call Parity - FINS3635 S2/2011 Put-Call Parity...

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- Put-Call Parity Matthias Thul * Last Update: September 14, 2011 This documents shows you how a the general put-call relationship for European options can be obtained by simple no-arbitrage arguments and gives some examples of how it can be applied. Derivation Consider a portfolio consisting of a long position in a European call option and a short position in a European put option and assume that both contracts have the same underlying asset, time to maturity T and strike price X . The terminal payoﬀ of this portfolio is max { S T - X, 0 } - max { X - S T , 0 } = max { S T - X, 0 } + min { S T - X, 0 } = S T - X. We observe that the payoﬀ of the option portfolio is equal to that of a long forward contract with a strike price of X . Furthermore, we remember from the lectures on forward contracts that the current value V 0 of a long position in an existing forward contract with strike price X is given by V 0 = ( F 0 - X ) e - rT , where F 0 is the fair delivery price of a forward contract with the same maturity as the two options. Remember that F 0 is being determined such that the initial value of the contract is zero. We can now argue that by the law of one price, two portfolios that have the same value at a future point in time need to have the same current value. Thus,

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## This note was uploaded on 03/02/2012 for the course MATH 172 taught by Professor Kong during the Fall '09 term at UCLA.

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DM3-Put-Call Parity - FINS3635 S2/2011 Put-Call Parity...

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