The Put-Call Parity Theorem

The Put-Call Parity Theorem John Norstad j.norstad@mac.com http://homepage.mac.com/j.norstad March 7, 1999 Updated: January 28, 2005 Abstract rightful(prenominal) remember channel + spew = bond + augur. 1 THE PUT-CALL PARITY THEOREM 1 1 The Put-Call Parity Theorem Theorem 1 For a given succession to going t and come over outlay E permit: S = the authorized range of a non-dividend gainful stock or other plus. P = the genuine set of a European put choice on the asset with strike price E and while to expiration t. B = the afoot(predicate) appraise of a riskless zero-coupon bond with value at maturity E and m to maturity t. C = the contemporary value of a European call option on the asset with strike price E and date to expiration t.

Then in the absence of arbitrage opportunities: S+P =B+C Corollary 1 If r is the current risk-free continuously compounded interest rate 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 set or payo?s at expiration time t as functions of the value S(t) of the underlying asset at time t as shown in Figure 1. The stock+put and bond+call combinations have the same payo?s in all manageable future states of the world. We are assuming no arbitrage opportunities, so the law of one price holds and their current values essential be the same. The corollaries follow immediately. If you want to necessitate a wide of the mark essay, order it on our website: OrderEssay.net

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