Volatility Smiles

‣ If there is a large one-day return it will increase the volatilityinstantaneously, but the estimate of volatility will stay raiseduntil N days later when that return drops out of the sample. Exponentially Weighted Moving Average‣ Now let us consider time-varying volatility. We don’t justhave one σ but must consider σ n , our estimate of the volatilityon the nth day, using data available up to that point.‣ Exponentially Weighted Moving Average estimates eliminatethe plateau-effect of the simpler moving average volatilityestimate.‣ The earlier models give every entry an equal weight whereasthis model weighs the most recent ones most and decays theweight exponentially as the returns become further.12