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Adiabaticity conditions for volatility smile in Black-Scholes pricing model

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  • L. Spadafora
  • G. P. Berman
  • F. Borgonovi

Abstract

Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price C(K) given the strike price K and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Scholes expression with volatility σ in the form of a volatility smile. We show that this approach based on a volatility smile leads to relative minima for the distribution function (“bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring “adiabatic" conditions on the volatility smile. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Suggested Citation

  • L. Spadafora & G. P. Berman & F. Borgonovi, 2011. "Adiabaticity conditions for volatility smile in Black-Scholes pricing model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 79(1), pages 47-53, January.
    • Handle: RePEc:spr:eurphb:v:79:y:2011:i:1:p:47-53
    DOI: 10.1140/epjb/e2010-10305-8
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    References listed on IDEAS

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    1. Allan M. Malz, 1997. "Option-implied probability distributions and currency excess returns," Staff Reports 32, Federal Reserve Bank of New York.
    2. Ulrich Kirchner, 2009. "Market Implied Probability Distributions and Bayesian Skew Estimation," Papers 0911.0805, arXiv.org.
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