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

Hans‐Jochen Bartels

Applied Stochastic Models in Business and Industry, 2000, vol. 16, issue 1, 1-9

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.

Date: 2000
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https://doi.org/10.1002/(SICI)1526-4025(200001/03)16:13.0.CO;2-E

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:16:y:2000:i:1:p:1-9

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