The

implied volatility in foreign exchange options trading is an indication of expected exchange rate volatility.

The following studies focused on regime switching of the

implied volatility index.

While the historical volatility of an asset return is readily computed from observed asset returns and the

implied volatility is computed from observed option price there may be inaccurate estimators of the volatility expected to prevail over a period of time.

Now, we are going to derive an approximated

implied volatility surface of second order in the log-moneyness.

The VIX is calculated using options on the S&P 500; thus, the same

implied volatility that is priced into options on the S&P 500 is used to power the VIX.

They test the relationship using multiple regression framework where realized volatility (RV) is regressed against non market maker demand for volatility along with a set of control variables (lags of RV, lags of

implied volatility, dummy for earning announcement date, stock volume and options volume).

Latane and Rendleman (1976) and Chiras and Manaster (1978) showed in their studies that weighted

implied volatility of the return of the stocks is a better estimator of future volatility than historical standard deviation.

Although Canina and Figlewski (1993) reported that

implied volatility has virtually no correlation with future return volatility and did not incorporate information contained in recent observed volatility, Christensen and Prabhala (1998) found that

implied volatility outperformed past volatility in forecasting future volatility and even subsumed the information content of past volatility in some of their specifications.

Day & Lewis (1992) and Lamoureux & Lastrapes (1993) concluded that

implied volatility is a biased and inefficient forecast of future volatility and that historical volatility contains more information about future volatility than does

implied volatility.

And while historical volatility has also fallen from its peaks, the decline in

implied volatility may say as much about the growing appetite for financial risk-taking as it does about expectations of the future volatility of oil prices.

After reviewing the main ideas in mathematical finance, this graduate textbook examine the calibration and the dynamics of the

implied volatility, which is the value of the volatility that, when put in the Black-Scholes formula, reproduces the market price for a European call option.

In 1993, the Chicago Board Options Exchange (CBOE) was the first exchange to introduce an

implied volatility index, called the VIX.