DerivativeHW2

# DerivativeHW2 - the futures and always be making money F-±...

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1. What this means is if you are buying the stock you pay the ask price (+ ± ) (the higher price) and if you are selling the stock you receive the bid price ( - ± ) (the lower price). Deﬁne r is the risk-free rate. Therefore ξ > r and r > θ , money is being borrowed a higher rate, then, ξ > θ Let F 0 = Actual futures price and F * = Theoretical futures price. We will show that the upper and lower bound for this contract is: ± S 0 - ± 2 ² e θ T F ± S 0 + ± 2 ² e ξ,T (1) case 1: F 0 > F * Cashﬂow ( t = 0) Cashﬂow ( t = T ) Sell Futures Contract 0 F 0 - f S T Borrow spot at lending rate S 0 = F 0 e - ξ T F 0 Buy underlying asset at spot - ± S 0 + ± 2 ² f S T Net Cash Flow F 0 e - ξ T - ± S 0 + ± 2 ² 0 Arbitrage exists when F 0 > ± S 0 + ± 2 ² e ξ T . The net cash ﬂow is always positive, so can buy the asset and short
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Unformatted text preview: the futures and always be making money. F-± S + ± 2 ² e ξ T > . case 2: F < F * Cashﬂow ( t = 0) Cashﬂow ( t = T ) Buy Futures Contract f S T-F Lend spot at lending rate-F e-θ T F Sell underlying asset at spot S-± 2 f S T Net Cash Flow ± S-± 2 ²-F e-θ T Arbitrage exists when F < ± S-± 2 ² e θ T . The net cash ﬂow is always positive. ± S-± 2 ² e θ T-F > 0, so shorting the asset and long position the futures....
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