is a main subject in mathematical finance with clear implications in physics. In 1900, five years before Einstein’s classic paper, Bachelier [@C64] proposed the [*arithmetic*]{} Brownian motion for the dynamical evolution of stock prices with the aim of obtaining a formula for option valuation. Samuelson [@PAS65] noticed the structural failure of Bachelier’s market model: it allowed negative values for the stock price, what led to undesired consequences in option prices. For correcting these unwanted features he introduced the [*geometric*]{} Brownian motion. Within his log-normal model, Samuelson obtained the fair price for perpetual options, although he was unable to find a general solution for expiring contracts. The answer to this question must wait until the publication of the works of Black and Scholes [@BS73], and Merton [@M73]. The celebrated Black-Scholes formula has been broadly used by practitioners since then, mainly due to its unambiguous interpretation and mathematical simplicity.

It is well established, however, that this model fails to fit some features of actual derivatives. In particular, there is solid evidence pointing to the necessity of relaxing the assumption, present in the Black-Scholes model, that a constant volatility parameter drives the stock price. Many models have been developed with the purpose of 