FINANCE
3_FF_Pricing_sol.pdf

T0 tt short sell forward 0 f s t borrow s e qt s e qt

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t=0 t=T Short-sell forward 0 F 0 -S T Borrow S 0 e -qT -S 0 e -qT e rT Buy and carry asset - S 0 e -qT S T Total payoff 0 F 0 -S 0 e (r-q)T >0 Fin330 26
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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 27
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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 Long forward 0 S T - F 0 Short-sell asset e -qT S 0 -S T Lend money -e -qT S 0 e -qT e rT S 0 Total payoff 0 e (r-q)T S 0 – F 0 >0 Fin330 28
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Investment asset with a known yield Fin330 29 For there to be no arbitrage, it must be the case that the price of the forward contract is F 0 = S 0 e (r-q)T
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Exercise l Consider a six-month forward contract on an asset with 3.96% yield per annum. The current asset price is $25, the risk free rate is 10% per annum. Assume all rates are expressed with continuous compounding. l What is the no-arbitrage forward price? l Suppose F 0 = 27, what is the arbitrary strategy? l Suppose F 0 = 23, what is the arbitrary strategy? 30 Fin330
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Exercise l No arbitrage price of forward is F 0 =. l An arbitrage opportunity exists: l If F 0 > S 0 e (r-q)T : l If F 0 < S 0 e (r-q)T : t=0 t=T Fin330 31
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Exercise l No arbitrage price of forward is F 0 =25.77. l An arbitrage opportunity exists: l If F 0 > S 0 e (r-q)T : Buy & borrow today + Short forward l If F 0 < S 0 e (r-q)T : Sell & lend today + Long forward t=0 t=T Buy asset today and borrow $ -25e -3.96%*0.5 25e -3.96*0.5 Own the asset: S T Pay back: -(25 e -3.96%*0.5 ) e *10%*0.5 Long forward 0 S T - F 0 Fin330 32
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