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On martingale diffusions describing the ‘smile‐effect’ for implied volatilities
Author(s) -
Bartels HansJochen
Publication year - 2000
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/(sici)1526-4025(200001/03)16:1<1::aid-asmb382>3.0.co;2-e
Subject(s) - martingale (probability theory) , econometrics , mathematics , economics , statistical physics , mathematical economics , physics
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.