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The Futures Market Model and No-Arbitrage Conditions on the Volatility

By Kristian R. Miltersen, J. Aase Nielsen and Klaus Sandmann
Working Papers
No. 03, November 2004

Interest rate futures are basic securities and at the same time highly liquid traded objects. Despite this observation, most models of the term structure of interest rate assume forward rates as primary elements. The processes of futures prices are therefore endogenously determined in these models. In addition, in these models hedging strategies are based on forward and/or spot contracts and only to a limited extent on futures contracts.

Inspired by the market model approach of forward rates by Miltersen, Sandmann, and Sondermann (1997), the starting point of this paper is a model of futures prices. Using the prices of futures on interest related assets as the input to the model, new no-arbitrage restricions on the volatility structure are derived. Moreover, these restrictions turn out to prevent an application of a market model based on futures prices.

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