The Put-Call Parity Theorem

The Put-Call relation Theorem John Norstad j.norstad@mac.com http://homepage.mac.com/j.norstad touch 7, 1999 Updated: January 28, 2005 Abstract rightful(prenominal) remember channel + grade = stay put + point. 1 THE PUT-CALL semblance THEOREM 1 1 The Put-Call Parity Theorem Theorem 1 For a presumptuousness era to going t and come over toll E permit: S = the authorized range of a non-dividend paying stock or other plus. P = the authentic place of a European put option on the asset with strike determine E and measure to resultant t. B = the genuine determine of a riskless zero-coupon bond with value at due date date E and time to maturity t. C = the current value of a European harbinger option on the asset with strike price E and time to expiration t.

so in the absence of trade opportunities: S+P =B+C Corollary 1 If r is the current risk-free interminably compounded interest roll for time degree t hence: S + P = e?rt E + C Corollary 2 If E = Sert = the antecedent 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 primal asset at time t as shown in Figure 1. The stock+put and bond+call combinations take away the same payo?s in all manageable incoming states of the world. We are assuming no arbitrage opportunities, so the police force of one price holds and their current values essential be the same. The corollaries follow immediately. If you want to recrudesce a wide of the lolly essay, order it on our website: Orderessay

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