The Black–Scholes model as a determinant of the implied volatility smile: A simulation study

Abstract

The paper represents an initial effort to shed light on the determinants of the implied volatility smile in financial (derivative) markets. It fully details the implications of the institutionalization of the Black–Scholes model in an uncertain world populated by individuals who are bounded by the amount of calculation or accounting which is technically possible. Combining model simulations, empirical analysis, and mathematical derivations, the paper proposes that the determinants of the volatility smile might be related to the behavior of traders. In pricing options, they use the widely accepted Black–Scholes formula with a measure of stock volatility that they derive from their subjective beliefs. Moreover, heterogeneity of traders’ beliefs and the way traders update their expectations have nontrivial effects, both on equilibrium prices and on the emergence of the implied volatility smile.