Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model
AbstractOur 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 (BS) expression with volatility 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1003.3316.
Date of creation: Mar 2010
Date of revision: Mar 2010
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-03-28 (All new papers)
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