  Options are financial instruments that depend on the underlying stock. We
explain their non-Gaussian fluctuations using the nonextensive thermodynamics
parameter $q$. A generalized form of the Black-Scholes (B-S) partial
differential equation, and some closed-form solutions are obtained. The
standard B-S equation ($q=1$) which is used by economists to calculate option
prices requires multiple values of the stock volatility (known as the
volatility smile). Using $q=1.5$ which well models the empirical distribution
of returns, we get a good description of option prices using a single
volatility.
