Volatility Smiles

Volatility Modeling‣ Since the Black-Scholes option pricing formulae requirevolatility as an input we need a way to accurately assess it.‣ Our understanding of volatility is that of meta-data that is nota real characteristic of an asset, but a descriptive one of itsprice. Given this difficulty, how can we best model it? Simple Models‣ The simplest way to account for volatility is assuming itconstant. However, it is clear that this approach isinapplicable to trading when examining real stock prices andtheir changing volatilities.‣ If we believe that the volatility is close to constant and onlyvaries slowly then we can consider the volatility of recentreturns only. Setting a window of N we have,‣ There are obvious major problems associated with thisvolatility measure; because the returns are equally weightedwe will get a plateau-effect associated with a large return.11