Volatility, Skew and Term Structure

This chapter reviews the concept of volatility of an asset and discusses realized volatility and implied volatility. Both of them give information about the asset and although they are related, they are different concepts. The realized volatility of an asset is the statistical measure known as the standard deviation. The implied volatility of the same asset, on the other hand, is the volatility parameter that one can infer from the prices of traded options written on this asset. The chapter highlights the measurements, uses, and limitations of realized volatility and implied volatility. It leads to the discussion of the implied volatility skew and the term structure of implied volatility in the chapter. The implied volatility surface is the three-dimensional surface obtained when one plots the market implied volatilities of European options with different strikes and different maturities. By fixing a maturity and looking at the implied volatilities of European options on the same underlying but different strikes, the implied volatility skew or smile is obtained, depending on its shape, typically specific to the asset class. Fixing a strike, usually the ATM strike, of options on the same underlying and looking at their implied volatilities, the term structure of volatilities is seen. The chapter also presents a non-technical treatment of various models that capture the different forms of volatility and skew and discusses the uses of these models.