Futures Options and the Volatility of Futures Prices

Authors

  • CLIFFORD A. BALL,

  • WALTER N. TOROUS

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    • The University of Michigan, and The University of Michigan and University of California-Los Angeles, respectively. We thank Fischer Black, Bradford Cornell, David Emanuel, Ronald Masulis, Mark Rubinstein, and an anonymous referee for helpful comments, and Thomas Thompson of the Chicago Board of Trade for useful discussions. Navin Chopra provided research assistance. Remote Computing Division of Hale Systems, Inc., supplied the data. This work was partially supported by research grants from the Graduate School of Business Administration at The University of Michigan and the Center for the Study of Futures Markets at Columbia University. Any remaining errors are the authors' responsibility.

ABSTRACT

Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at-the-money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.

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