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Valuation of a Forward Contract or FRA

A futures contract is similar to a forward contract in that it is an agreement to buy or sell an asset for a specified price on a specified date. But such a contract is traded on an organized exchange and is mark-to-market. A futures contract also differs from a forward contract in that parties to a futures contract must deposit an initial margin at inception of contract, and, subsequently, adjust the cash margin according to the change of the "market value" of the contract. The margin variation is the daily variation of the value of the contract. It is paid to the clearinghouse by the party showing a loss and credited to the party showing a gain. Futures markets are detailed elsewhere and we focus here on the valuation of a forward contract that is over-the-counter (OTC).

The mark-to-market value of an interest rate forward contract (FRA) is derived from the differential between forward and spot rates. At inception, we lend and borrow the same amount. Intuitively, the value should be zero. Formally, the value is zero because the market values equivalently the forward rate and the uncertain spot rate. After inception, when time passes, the contracted flows from lending - borrowing remain constant, but not the interest rates. Since the forward contract is a made of two positions, long 2-year and short 1-year, its value is the net value of these two zero coupon bonds at t, after date of inception 0 and before date 1:

Note that discounting is from cash flow date 1 until current date t. We assume here that the contract is settled at time 1, when the spot rate at 1 is known. By definition, the portfolio value at inception date is 0. After the initial date, the cash flows remain fixed, but not the interest rates. Therefore, the net value of the two positions fluctuates and might become positive or negative. The one which owns the positive value would lose it if the counterparty defaults. This random exposure to credit risk is discussed in the chapter on counterparty risk (Chapter 44).

 
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