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Unformatted text preview: Chapter 3 Forward Contracts and Put-Call Parity Recall that a forward contract is an agreement between two parties made at some time τ concerning the sale of an asset at a future time T , called the delivery time , delivery date , or maturity . The party taking the long position agrees to buy a prescribed amount of the asset on the delivery date from the counterparty, who takes the short position , at a price F , called the forward price . The party taking the short position agrees to sell the asset at time T at the price F . The forward price is agreed upon at time τ and neither party pays anything to enter into the agreement. It is customary to scale F so that it represents the forward price per unit of the asset. Although the forward price is chosen so that the value of both positions is zero at time τ , both positions will generally have nonzero values at times t with τ < t ≤ T . The values of the two positions will always have the same magnitude, but opposite signs. In particular, at time T , the value (per unit) of the long position is S T- F and the value (per unit) of the short position is F - S T , where S T is the price (per unit) of the underlying asset at time T . At times after the contract is initiated, F is often referred to as the delivery price in order to avoid confusion with the forward price in contracts being issued currently. In situations when there could be ambiguity concerning the time at which the contract was initiated, or the delivery time, we shall use the notation F τ,T in place of F . Many people use the phrase “buy a forward contract” to mean “take the long position on a forward contract” and the phrase “sell a forward contract” to mean “take the short position on a forward contract”. In these notes, we shall always use the more formal terminology “take a long position” and “take a short postion”. Forward contracts have existed since ancient times. They can potentially remove risk for both parties. However, there are some practical difficulties that limit their use in real-world financial markets. For example, it may not be easy for an individual 81 wanting to take a position on a forward contract to find a party who wants the counterposition for the same quantity and delivery date of the asset. Another serious concern is that one of that parties may be unable to fulfill their obligation on the delivery date. In practice, it is much more common to use a closely related kind of contract called a futures contract . The main difference between futures and forwards is the manner in which settlement is made. Futures contracts are more complicated to analyze mathematically; they will be discussed briefly in Section 3.6 and treated treated in detail in 21-370. Although they are used only sparingly in the real world, it is extremely useful to study forward contracts. In particular, forward contracts will be helpful in analyzing put and call options. Moreover, if interest rates are deterministic,helpful in analyzing put and call options....
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- Spring '10
- Forward price