Implied Volatility Functions: Empirical Tests

Authors

  • Bernard Dumas,

    1. Hautes Études Commerciales (HEC) School of Management, Fuqua School of Business, Duke University, National Bureau of Economic Research (NBER), Center for Economic Policy Research (CEPR)
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  • Jeff Fleming,

    1. Jones Graduate School of Administration, Rice University
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  • Robert E. Whaley

    1. Fuqua School of Business, Duke University
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    • Bernard Dumas is Professor of Finance, Hautes Études Commerciales (HEC) School of Management, Research Professor of Finance, Fuqua School of Business, Duke University, National Bureau of Economic Research (NBER) Research Associate, and Center for Economic Policy Research (CEPR) Research Fellow; Jeff Fleming is Assistant Professor of Administrative Science, Jones Graduate School of Administration, Rice University; and, Robert E. Whaley is T. Austin Finch Foundation Professor of Business Administration, Fuqua School of Business, Duke University.

      This research was supported by the HEC School of Management and the Futures and Options Research Center at the Fuqua School of Business, Duke University. We gratefully acknowledge discussions with Jens Jackwerth and Mark Rubinstein and comments and suggestions by Blaise Allaz, Denis Alexandre, Suleyman Basak, David Bates, Greg Bauer, Peter Bossaerts, Andrea Buraschi, Peter Carr, Gilles Demonsant, Jin-Chuan Duan, Bruno Dupire, Gary Gorton, Sanford Grossman, Bruce Grundy, Philippe Henrotte, Steve Heston, John Hull, Eric Jacquier, Jean-Paul Laurent, Hayne Leland, Angelo Melino, Krishna Ramaswamy, Ehud Ronn, Hersh Sheffrin, Robert Stambaugh, Denis Talay, Ken West, Alan White, Stanley Zin, three anonymous referees, René Stulz (the editor) and the seminar participants at HEC, the Isaac Newton Institute, Cambridge University, the Chicago Board of Trade's Nineteenth Annual Spring Research Symposium, the University of Pennsylvania, the University of New Mexico, the University of Toronto, Hong Kong Polytechnic University, the University of New South Wales, the Sixth Annual Conference on Financial Economics and Accounting at the University of Maryland, the Inquire Europe group in Barcelona, the London Business School, the NBER Asset Pricing group, the European Financial Management Association meeting in Innsbruck, the University of British Columbia, the University of Toulouse, the “World of Fischer Black” London School of Economics/London School of Business conference in Sardignia, Erasmus University, Rice University, the University of Amsterdam, the University of Lausanne, and the Dallas meetings of the Institute for Operations Research and the Management Sciences.


Abstract

Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) hypothesize that asset return volatility is a deterministic function of asset price and time, and develop a deterministic volatility function (DVF) option valuation model that has the potential of fitting the observed cross section of option prices exactly. Using S&P 500 options from June 1988 through December 1993, we examine the predictive and hedging performance of the DVF option valuation model and find it is no better than an ad hoc procedure that merely smooths Black–Scholes (1973) implied volatilities across exercise prices and times to expiration.

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