ArbitrageProofForPut-CallParityandMinimumValue

# ArbitrageProofForPut-CallParityandMinimumValue - Arbitrage...

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Arbitrage Proofs for Put-Call Parity and Minimum Value 1 I. Put-Call Parity Put-call parity states that C = S - Ee - rT + P (1) To prove this statement, assume that it doesn’t hold and show that it is possible to make riskless proﬁts. We will use numbers for concreteness. Assume S = \$110, E = \$100, t = 1, r = 0. Also assume C = \$12 and P = \$5. Thus the call is undervalued and/or the put is overvalued, given S = \$110 and E = \$100. Construct an arbitrage by buying the “cheap” call at \$12 and selling the “expen- sive” put at \$5. Recall that long a call and short a put both proﬁt when S rises. Therefore, we complete the arbitrage by selling S short at \$110. Our portfolio today: Cash ﬂow Buy 1 call - \$ 12 Short (write) 1 put + \$ 5 Sell short 1 share + \$110 Invest proceeds -\$103 Net 0 Examine what happens on expiration (1 year from now) if S > E and if S < E . If S E : Exercise call -\$100 Deliver against short - Put expires worthless 0 Receive proceeds from investment \$103 \$3 1 Notes for Finance 100 (sections 301 and 302) prepared by Jessica A. Wachter.

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ArbitrageProofForPut-CallParityandMinimumValue - Arbitrage...

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