Can anyone explain to me the difference between implied, realised and historical volatility? I thought realised and historical volatility are pretty much the same. Also i thought the volatility implied by GARCH(1,1) is type of implied volatility. Am i correct? thanks

Realized and historical are the same thing, just different terms. The term statistical volatility is also used. Implied volatility is the volatility that is implied in the market option prices. That is, you take an option pricing model, such as Black Scholes, and then stick in the current market option price along with the other variables and solve for volatility. Hence the term implied volatility. The volatility number you get from Garch (1,1) would be a volatility forecast.

The relationship between implied and realized volatility http://www.cls.dk/caf/wp/wp-23.pdf Q 1.3 REALIZED AND HISTORICAL VOLATILITY In this study, we want to examine the relationship between volatility implied by an option price and subsequently realized index return volatility. We therefore need to construct a time series of realized volatility. Each realized volatility is calculated as the standard deviation of the daily index returns during the remaining life of the option, the period covered by the implied volatility. ... 3 Conclusion We have in this paper studied whether volatility implied by the Danish KFX index call and put option prices predict future realized index return volatility. To our knowledge this question has not been examined previously. We find that historical return volatility does not add any information beyond that in implied volatility. This is so even though we have included more information in the historical volatility measure than the simple lagged realized volatility. Hence, we cannot reject the hypothesis that the volatility implied by one month at-the-money call or put KFX option prices is an efficient albeit slightly biased estimator of realized return volatility. This result provides support for the use of option pricing theory even for KFX options and might not have been anticipated, given the relative illiquidity of the Danish market. The analysis shows that the KFX option market perhaps surprisingly shares some efficiency features with the largest option market, that for OEX options on the S&P 100 index. Due to infrequent trading of the KFX options, in some months either put option prices or call prices do not meet the arbitrage boundaries. We therefore introduce a common implied volatility which includes information from both call and put prices, in such a way that we do not get any missing observations. We find that this implied volatility measure is an even better forecast of future realized return volatility than either of the separate call and put implied volatilities: It is efficient, significant even in the multiple regression where historical volatility is also included, the bias is insignificant, and there is no problem with missing observations. We have therefore at the same time constructed a method for forecasting realized return volatility in a market characterized by infrequent option trading. UQ