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Published byRose Lyons Modified over 9 years ago
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Put-Call Option Interest Rate Parity
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Objective Determine the international parity relationship between Call, Put, and Forward prices
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Outline Two arbitrage portfolios Derivation of parity conditions Exemplification
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Two arbitrage portfolios Consider: C: the premium of a call option on the Sfr P: the premium of a put option on the Sfr X: the strike price of call and put options ni Sfr : Sfr nominal interest rate ni $ : $ nominal interest rate s = $/Sfr : spot exchange rate f = forward rate
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Two arbitrage portfolios e = $/Sfr
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Two arbitrage portfolios s = $/Sfr
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Parity conditions derived It follows that C = s 0 /(1+ni Sfr ) - X/(1+ni $ ) +P According to interest rate parity we know that s 0 /(1+ni Sfr ) = f 1 /(1+ni $ ) Hence, if we are in Canada, C = (f 1 - X)/(1+ni $ ) + P In general, C = (f 1 - X)/(1+ni h ) + P
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Exemplification e 0 = C$0.7143/Sfr ni $ = 3.5% ni Sfr = 4.4% One-year forward = C$0.70814/Sfr A call on the Sfr struck at C$0.701/Sfr, expiring in one year sells at C$0.035/Sfr A put on the Sfr struck at C$0.701/Sfr, expiring in one year sells at C$0.023/Sfr
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Note C$0.70814/C$0.7143 = (1.035)/(1.044) IRP holds C$0.035 > C$(0.70814-0.701)/(1.035) + C$0.023 Arbitrage opportunity
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Another two arbitrage portfolios
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Analysis At expiration, the combined payoff from the two portfolios is always zero. However, buying the first portfolio and shorting the second one has produced an arbitrage profit of (C$2,940- C$2,511.25)=C$428.75 up-front.
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