2. Put-Call Option Interest Rate Parity

3. Objective Determine the international parity relationship between Call, Put, and Forward prices

4. Outline Two arbitrage portfolios Derivation of parity conditions Exemplification

5. 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

6. Two arbitrage portfolios e = $/Sfr

7. Two arbitrage portfolios s = $/Sfr

12. 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

13. 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

14. 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

15. Another two arbitrage portfolios

19. 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.