Why is volatility important? Volatility is indispensable and is fundamental to pricing any asset within the financial market, from a single security to the most complicated derivative. It is quite important when managing portfolios or in calculating risk or the corresponding hedging strategy, but the problem is that it is not observable and it is heteroskedastic, it fluctuates over time, you should not assume a homoscedastic pattern, constant over time, because it will a huge error during the estimation. For this reason, enormous literature has made enormous efforts in trying to predict future volatility as accurately as possible, so a large number of sophisticated models have been created since the crucial study by Engle (1982), where he introduced the ARCH model. Since financial variables are characterized by a nonlinear dependence, the ARCH model captures such dependence because it allows for heteroscedasticity, namely, it depends only on the latest lag. However, when the sample is considerably large, the ARCH model is unable to capture this dependence because so many lags will be needed that the estimation becomes too complex. Subsequently, however, Bollerslev (1986) introduced the GARCH model. The main advantage is that it is able to capture the memory of volatility, that parameter is beta allowing for large sample sizes. The main problem is that you define a symmetric response in volatility, in other words, you only take into account the magnitude of the shocks, rather than the sign, which means that, for the same magnitude, negative and positive shocks will have the same effect. . This is known as leverage and extensive empirical evidence has shown that it is present in financial variables, although it is not as significant for exchange rates. good enough, the GARCH model addresses two problems that will appear during estimation. (1) Symmetrical response to volatility, known as leverage, which is quite well resolved with the use of other more sophisticated GARCH-type models, in this case they suggest the TGARH, although they note that this effect is not too significant in the case of exchange rates. (2) Constant volatility, they introduce the GARCH component which allows the possibility of introducing volatility models varying over time, a characteristic which is unachievable with the estimate of a GARCH which only allows a path back to the mean. Ultimately, the conclusion is that the GARCH model beats the statistical ones for most exchange rates, this result is linked to the evidence reached by Andersen and Bollerslev (1998) and Andersen et al. (1999)