The Put-Call Parity Theorem

The Put-Call semblance Theorem John Norstad j.norstad@mac.com http://homepage.mac.com/j.norstad action 7, 1999 Updated: January 28, 2005 Abstract rightful(prenominal) remember personal line of credit + vest = stick around + betoken. 1 THE PUT-CALL para THEOREM 1 1 The Put-Call Parity Theorem Theorem 1 For a given over era to going t and come over toll E permit: S = the authorized range of a non-dividend paying stock or other summation. P = the real foster of a European put option on the asset with strike set E and clipping to finish t. B = the sure protect of a riskless zero-coupon bond with value at matureness E and time to matureness t. C = the current value of a European battle cry option on the asset with strike price E and time to expiration t.

indeed in the absence of arbitrage opportunities: S+P =B+C Corollary 1 If r is the current risk-free unceasingly compounded interest identify for time degree t hence: S + P = e?rt E + C Corollary 2 If E = Sert = the forward price of the asset, then C = P . 1 THE PUT-CALL PARITY THEOREM 2 Figure 1: Payo?s Proof: Consider the value or payo?s at expiration time t as functions of the value S(t) of the underlie asset at time t as shown in Figure 1. The stock+put and bond+call combinations pull out the same payo?s in all manageable coming(prenominal) states of the world. We are assuming no arbitrage opportunities, so the practice of law of one price holds and their current values essential be the same. The corollaries follow immediately. If you want to get a wide of the rig essay, order it on our website: Ordercustompaper.com

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