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On martingale diffusions describing the ‘smile‐effect’ for implied volatilities

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  • Hans‐Jochen Bartels

Abstract

This paper discusses diffusion models describing the ‘smile‐effect’ of implied volatilities for option prices partly following the new approach of Bruno Dupire. If one restricts to the time homogeneous case, a careful study of this approach shows that the call option prices considered as a function of the price x of the underlying security, remaining time to maturity T–t and strike price K have necessarily to satisfy a certain functional equation, in order to fit into a coherent model. It is shown that for certain examples of empirically observed option prices which are reported in the literature, this functional equation does not hold. © 2000 John Wiley & Sons, Ltd.

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  • Hans‐Jochen Bartels, 2000. "On martingale diffusions describing the ‘smile‐effect’ for implied volatilities," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 16(1), pages 1-9, January.
    • Handle: RePEc:wly:apsmbi:v:16:y:2000:i:1:p:1-9
    DOI: 10.1002/(SICI)1526-4025(200001/03)16:13.0.CO;2-E
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    1. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84, January.
    2. Schmitt, Christian, 1996. "Option pricing using EGARCH models," ZEW Discussion Papers 96-20, ZEW - Leibniz Centre for European Economic Research.
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