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Unformatted text preview: EC3070 FINANCIAL DERIVATIVES PRESENT VALUES The Initial Value of a Forward Contract . One of the parties to a forward contract assumes a long position and agrees to buy the underlying asset at a certain price on a certain specified future date denoted t = τ . The other party assumes a short position and agrees to sell the asset on the same date. The date when the contract is made is t = 0. The agreed settlement price is K τ = F τ | , where F τ | denotes the price at time t = 0 for a delivery of the asset at time t = τ . Let t = 0 be the current time so that S is the spot price of an asset. Let the current risk-free rate of compound interest be r . Then, the spot price and the forward price are related by the formulae (i) F τ | = S e rτ and (ii) S = F τ | e − rτ . Here, we understand that the forward price F τ | must be discounted by the factor e − rτ to equate it to the present value of S . Equally, if the sum of S were to be invested for τ periods under a regime of compound interest, then it would grow to S e rτ . To establish the necessity of the relationships, we may consider how, in their absence, there would be possibilities for arbitrage, which may be ruled out by assumption. Imagine that S e rτ > F τ | . An investor could sell the asset today for S and invest the proceeds to derive a sum of S e rτ at time τ . At the same time, he could enter a long forward contract to buy the asset at time τ for F τ | . In this way, he would derive a riskless arbitrage profit of...
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- Spring '12
- Derivative, Forward contract, Fτ, Fτ |0