T0 tt long forward 0 s t f 0 short sell the asset s 0

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What could investors do? t=0 t=T Long forward 0 S T -F 0 Short-sell the asset S 0 -S T Lend money -S 0 S 0 e rT Total payoff 0 S 0 e rT -F 0 Fin330 18
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Arbitrage opportunities l There would be an arbitrage opportunity in t=T (“money tomorrow”). l This is called “reverse cash and carry” arbitrage: l short-sell the underlying asset and l long the forward contract. Fin330 19
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Arbitrage opportunities Fin330 20 For there to be no arbitrage, it must be the case that the price of the forward contract is F 0 = S 0 e rT .
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Overview 1. Types of the underlying assets. 2. Pricing of forwards, when the underlying asset generates no income. 3. Pricing of forwards, when the underlying asset generates a known yield. Fin330 21
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Investment asset with a known yield l Asset generates a cont. compounded yield q % p.a. l Buying e -qT units of asset today gives 1 unit at maturity. l Consider again two ways of acquiring an asset that you will need 6 months from now: 1. Buy it today (taking into account the yield) and hold it. 2. Long a 6-month forward contract today. l Think intuitively if the price F 0 must be higher or lower as compared to the case studied before. Fin330 22
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Investment asset with a known yield l Compare the payoffs at t=T : l Buy asset now : l Long forward: t=0 t=T Buy e -qT assets today and borrow $ Long forward Fin330 23
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Investment asset with a known yield l Compare the payoffs at t=T : l Buy asset now: S T - S 0 e (r-q)T ; l Long forward: S T – F 0 . t=0 t=T Buy e -qT assets today and borrow $ -S 0 e -qT +S 0 e -qT =0 Own the asset: S T Pay back: - S 0 e -qT e rT Long forward 0 Own asset: S T Pay forward price: - F 0 Fin330 24
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Arbitrage opportunities l Suppose that S T - S 0 e (r-q)T > S T – F 0 F 0 > S 0 e (r-q)T l What could investors do? t=0 t=T Total payoff Fin330 25
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Arbitrage opportunities l Suppose that S T - S 0 e (r-q)T > S T – F 0 F 0 > S 0 e (r-q)T l What could investors do?
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