ABSTRACT
This chapter is devoted to the concepts of spot (instantaneous) volatility, historical volatility (computed from the standard deviation of the log-returns), and implied volatility (the volatility that has to be used in the Black-Scholes-Merton equation to get the option market price). We also study the plot of the implied volatility as a function of the strike and time to maturity (the implied volatility surface), that exhibits smile and skew effects that flatten with time to maturity.
