Modelling and exploring the dynamics of financial assets' volatility has been the main issue and central focal point among finance academics and practitioners. Volatility is fundamental for risk management, option pricing, hedging of derivatives positions and policy making.
Most previous research has focused on historical volatility, but recently implied volatility has received attention due to some breakthrough studies, such as Christensen and Probhala (1998), Fleming (1998), and Dumas, Fleming and Whaley (1998). They show that implied information is superior to historical when forecasting volatility and further point out that a precise notion of the market's judgment and expectation of volatility is vital.
For instance, to develop expectations about volatility based on past behaviour of stock prices and other relevant information is backward-looking and called historical volatility. In contrast, implied volatility is forward looking, that is implied by market prices of options. Option prices are the common consensus of the market participants about the expected future volatility.
Therefore, implied volatility is the market expectation about the average future volatility of the underlying asset over the remaining life of an option. The volatility expectation of market participants can be recovered by inverting the option-pricing formula. However, it is well known that after the October 1987 market crash, implied volatility computed from the options’ prices on stock indexes appears to be different across strikes and term structure, if examined at the same time, for example, the same day. This implies that implied volatilities present a two-dimensional surface whose dynamics across strikes and over time has to be examined.