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Currency Derivatives

Currency Derivatives. Steven C. Mann The Neeley School of Business at TCU Finance 70420 – Spring 2004. Currency Exposure. U.S. firm buys Swiss product; invoice: SF 62,500 due 120 days Spot rate S 0 = 0.7032 $/SF. $ invoice cost. If rate at day 120 (S 0+120 )

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Currency Derivatives

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  1. Currency Derivatives Steven C. Mann The Neeley School of Business at TCU Finance 70420 – Spring 2004.

  2. Currency Exposure U.S. firm buys Swiss product; invoice: SF 62,500 due 120 days Spot rate S0 = 0.7032 $/SF $ invoice cost If rate at day 120 (S0+120) rises, purchase cost rises: (S0+120) cost .6532 $40,825 .7032 43,950 .7532 47,075 S0+120

  3. Forward Hedge of Currency Exposure Enter into forward contract to buy SF 62,500 in 120 days. Forward exchange rate is f0,120($/SF). Choose forward rate so that initial value of contract is zero. How is forward rate determined? Need additional information: 120 day $ riskless interest rate r$ 120 day SF riskless interest rate rSF Need to find cost today of 1 dollar 120 days from now 1 Swiss franc 120 days from now. E.g. T-bill price = price of dollar to be received at bill maturity

  4. Zero-coupon bond prices discount rates (id): B(0,T) = 1 - id (T/360); where id is ask (bid) yield simple interest rates (is): B(0,T) = 1/ ( 1 + is x (T/365))

  5. Find B$(0,120) and BSF(0,120) Need to find cost today of 1 dollar 120 days from now 1 Swiss franc 120 days from now. Given: simple 120 day interest rates: r$ = 3.25% rSF = 4.50% then B$ (0,120) = ( 1 + .0325 x (120/365)) -1 = $ 0.9894 BSF(0,120) = ( 1 + .0450 x (120/365)) -1 = SF 0.9854

  6. Forward rate determination: absence of arbitrage Strategy One (cost today = 0): Long forward contract to buy SF 62,500 at f0,120 at T=120 value of forward at (T=120) = 62,500 x ( S120 - f0,120) dollars Strategy Two (cost today depends on forward rate): a) Buy PV(62,500) SF, invest in riskless SF asset for 120 days cost today = S0($/SF) x BSF(0,120) x SF 62,500 b) Borrow PV($ forward price of SF 62,500) at dollar riskless rate: borrow today: 62,500 x f0,120 x B$(0,120) dollars pay back loan in 120 days: f0,120 x 62,500 dollars total cost today of strategy two = cost of (a) + cost of (b) = 62,500 x [0.7032 x BSF(0,120) - f0,120 x B$(0,120) ] payoff of strategy two at (T=120): a) 62,500 SF x S120 ($/SF); b) repay loan: - f0,120($/SF)x 62,500 net payoff = 62,500 x ( S120 - f0,120) dollars

  7. Forward rate determination: absence of arbitrage Strategy one: position cost today payoff 120 days later long forward 0 62,500SFx (S120 - f0,120) dollars Strategy two: position cost today payoff 120 days later buy SF bill62,500 SFx S0BSF(0,120)62,500 SF x S120 ($/SF) dollars borrow PV of forward price - 62,500 SFx f0,120 B$(0,120) -62,500 SF x f0,120 dollars net 62,500 x 62,500SFx (S120 - f0,120) dollars (S0BSF(0,120) - f0,120 B$(0,120)) Strategies have same payoff must have same cost: 0 = S0BSF(0,120) - f0,120 B$(0,120)

  8. Interest rate parity Interest rate parity: f0,120 B$(0,120) = S0 BSF(0,120) f0,120 ($/SF) = S0($/SF)x this can be written: f0,120 ($/SF) = S0($/SF) x if we use continuously compounded interest rates, this can be written: f0,120 ($/SF) = S0($/SF) x BSF(0,120) B$ (0,120) (1 + r$ x (120/365)) (1 + rSF x (120/365)) (1 + r$ ) (120/365) (1 + rSF) (120/365)

  9. Forward rates via Interest rate parity Interest rate parity: f0,120 B$(0,120) = S0 BSF(0,120) f0,120 ($/SF) = S0($/SF)x= 0.7032 = 0.7032 (.99596) = 0.70035 BSF(0,120) 0.9854 B$ (0,120) 0.9894 Interest rates Forward exchange rates: r$> rforeignf 0,T> S0 r$ < rforeignf 0,T< S0

  10. Example Data: S0 = 0.6676 ($/DM) 180 day T-bill price = $ 98.0199 per $100 180 day German bill price = DM 96.4635 per DM100 180 day forward rate = f0,180 = 0.660 $/DM Find theoretical forward rate: Interest rate parity: f0,180 B$(0,180) = S0BDM(0,180) f0,180 ($/DM) = S0($/DM)x= 0.6676 = 0.6676 (.98412) = 0.6570 BDM(0,180) 0.964635 B$ (0,180) 0.980199 Is there arbitrage opportunity?

  11. Exploit arbitrage opportunity Data: S0 = 0.6676 ($/DM) 180 day T-bill price (B$(0,180)) = $ 98.0199 per $100 180 day German bill price (BDM(0,180)) = DM 96.4635 per DM100 180 day forward rate = f0,180 = 0.660 $/DM Determine that theoretical forward rate is 0.6570 $/DM: Arb strategy: position cash today payoff 180 days later sell forward 0 - (S180 - f 0,180)x(size) buy DM bill - S0($/DM)x (BDM(0,180) x (size)DM x (size) x S180 ($/DM) borrow $ cost of DM bill + S0($/DM)x (BDM(0,180) x (size) -S0BDM(0,180)x(size)x(B$(0,180))-1 net 0 (size) x f0,180 - S0 BDM(0,180) B$(0,180) Payoff = (0.660 -0.657) x (size) e.g. 1 million DM gives (.003) x 1,000,000 = $3,000 profit

  12. Currency Options Example: Buy spot DM call option with strike K = $0.64/ DM option size is 62,500 DM, option life 120 days. Option premium is $0.0062 per mark ( 0.62 cents/DM) Option payoff 0 .61 .62 .63 .64 .65 .66 S0+120 ($/DM)

  13. Forward vs. Option hedging U.S. firm buys machinery, cost is DM1 million, due 120 days. Hedge: buy DM 1 million forward at $0.64/DM; or : buy 16 calls, K = $0.64/ DM, @ 0.62 cents/DM) ($6,200) Option cost includes $83 = 6200( 1 + .04 x 120/360) financing cost

  14. Hedge outcomes Net cost of equipment unhedged 660,000 650,000 640,000 630,000 620,000 610,000 600,000 Option hedge Forward hedge .60 .61 .62 .63 .64 .65 .66 S0+120 ($/DM)

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