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.

Spadafora, L., Berman, G. P., Borgonovi, F., Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model, <<THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS>>, 2010; 2010 (8): N/A-N/A. [doi:DOI: 10.1140/epjb/e2010-10305-8] [http://hdl.handle.net/10807/3620]

Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model

Spadafora, Luca;Berman, Gennady P.;Borgonovi, Fausto
2010

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.
Inglese
Spadafora, L., Berman, G. P., Borgonovi, F., Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model, <<THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS>>, 2010; 2010 (8): N/A-N/A. [doi:DOI: 10.1140/epjb/e2010-10305-8] [http://hdl.handle.net/10807/3620]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/3620
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