interest rate parity

# they are nice for short hand but not sufficiently

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Unformatted text preview: 360 1st The equation is easiest to work with The 2nd equation has the better intuition I. Find any one of F, S, i, i* II. If there is a CIRP violation, find the arbitrage that will make a profit, or III. Find the better location to borrow or lend 62 13 Examples € ¥ £ \$ Data: Spot rate 3 m. LIBOR 1.5921 \$/€ 4.96% 107.00 ¥/\$ 0.75% 1.9918 \$/£ 5.77% n.a. 2.30% 63 \$/€ A “fair” quote on a 3-month forward contract is: Ft,90 = 1.5921(1+0.0230/4)/(1+0.0496/4) = Which currency is at a premium? 64 ¥/\$ A “fair” quote on a 3-month forward contract is: Ft,90 = = Which currency is at a premium? 66 14 \$/£ A “fair” quote on a 3-month forward is: Ft,90 = = Which currency is at a premium? 68 \$/£ If Ft,90 = 1.96, what would be the implied £ interest rate? 1+i£t,90 = i£t,90 = 70 Arbitrage The most accurate predictions in finance rely on arbitrage! CIRP is an arbitrage relation, so we’d expect CIRP to hold very well • And it does! What is the nature of the arbitrage? • We’ll do this without bid-ask spreads; with them it is a lot messier See the appendix in my posted note if very interested 72 15 Synthesizing a Forward Position A Forward contract delivers 1 fc T days from now. Is there another way to get 1 fc T days ahead? 74 Synthesizing a Forward Position A Forward contract delivers 1 fc T days from now. Is there another way to get 1 fc T days ahead? You could take the money in \$s, convert it to fc now, and deposit it in a T-day fc account The difference between this and a Forward is that you have to come up with the money now 75 Synthetic Forward (cnt.) We can fix this by borrowing in \$s for T days Now it is the same as the Forward: Forward contract: • T days from now you deliver \$s • You receive 1 fc Synthetic Forward: • T days from now you pay off the \$ loan (pay \$s) • Your 1 fc deposit matures (receive fc) 76 16 Synthetic Forward (cnt.) Day 0: Borrow \$ Purchase S0 * 1 i 0,T S0 1 1 fc in the market * * * 1 i0,T S 0 1 i0,T * Deposit them in an fc account at i0,T 77 Synthetic Forward (cnt.)...
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