Redfield
hile many futures contracts' theoretical prices can be determined by using W cost of carry models, the valuation of the U.S. Dollar Index futures contract must consider the volatility of the underlying index despite the fact that the contract has no optional characteristics. Because of the method of calculation of the Dollar Index futures contract, the contract should be awarded a volatility premium. If the premium is not implicit in the contract price, riskless arbitrage may be possible.
This article attempts to prove the need for a volatility premium and to calculate the magnitude of that premium.
Over the past several years, the concept of estimated volatility has become accepted in the financial community as a necessary parameter to value options or financial instruments with imbedded options (e.g., callable bonds and mortgagebacked securities). The importance of volatility in determining option value is proved in the Black-Scholes option pricing model and other option pricing models.
Volatility can also affect the value of financial instruments without optional components. One interesting example is the pricing of the U.S. Dollar Index (USDX) futures contract.
The USDX contract is a relatively new futures contract being traded on the Financial Instruments Exchange (a division of the New York Cotton Exchange).
The USDX is a geometrically weighted index of the currencies of ten major trading partners of the United States.
I would like to thank Jim Meisner, John Richards, and Professor Ted Day for their comments, without implicating them in any errors contained herein.