Objective Determine the international parity relationship between Call, Put, and Forward prices
Outline • Two arbitrage portfolios • Derivation of parity conditions • Exemplification
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 niSfr : Sfr nominal interest rate ni$ : $ nominal interest rate s = $/Sfr : spot exchange rate f = forward rate
Parity conditions derived It follows that C = s0/(1+niSfr) - X/(1+ni$) +P According to interest rate parity we know that s0/(1+niSfr) = f1/(1+ni$) Hence, if we are in Canada, C = (f1 - X)/(1+ni$) + P In general, C = (f1 - X)/(1+nih) + P
Exemplification e0 = C$0.7143/Sfr ni$ = 3.5% niSfr = 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
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
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.