Why is important the volatility?
Volatility is indispensable, and is central for pricing any asset within the financial market, from a single stock to the most complicated derivative. It is quite important when managing portfolios or in computing the risk or the corresponding hedging strategy, but the issue is that is not observable and it is heteroskedastic, it fluctuates through time, you should not assume a homoscedastic pattern, constant over time, because it will be a huge mistake when estimating. For that, enormous literature has put huge effort in trying to predict future volatility as accurately as possible, thus large number of sophisticated models has been created since the ...view middle of the document...
Therefore, since the seminal paper of Bollerslev, many authors have tried to refine the base GARCH, accommodating for leverage effect among other improvements.
On the other hand, the Stochastic Volatility literature is one of the most well known statistical approaches for estimating future volatility.
Supplement approaches are those than connect specific information of the underlying, but the final estimation is only valid under that specifics assumptions. We could think about the Black & Scholes method for getting the price of an option, of the VaR model that requires the estimation of the volatility.
The papers that are presented below suggest that, in general, the GARCH model performs reasonable well in forecasting. Although there are some studies that find that the GARCH predictions are not so well, many authors have found later on that this bad performance was due to the bad specification of the ‘real’ volatility and not to the GARCH estimation per se, because the conditional variance of a financial series is an unobservable process, so there are some possible interpretations of what are you going to substitute in order to do the forecasting exercise. The literature presented in this paper also notices the differences when using different proxies for the conditional volatility.
This project is organized as follows; sections 2 to 5 are a simple summary of the key references that I have received. Section 6 includes some personal comments about the overall literature studied and finally, Section 7 is a briefly conclusion of the topic.
2. A Forecast Comparison Of Volatility Models: Does Anything Beat A GARCH (1,1)?
In this paper, they wanted to know if some sophisticated volatility models work much better than the naive GARCH (1,1) when trying to capture the conditional variance, therefore they propose 330 GARCH-type models in order make a ranking of which ones perform better.
The study was done with two different financial series; an exchange rate, the Deutsche Mark against the US dollar, and the IBM stock, both of them in daily frequency.
As they wanted to know the ability for each model in predicting the future conditional variance, the overall sample is divided into estimation or in-sample period and an evaluation or out-of-sample period. For the exchange rate, the estimation stage covers from October 1987 to September 1992, and the evaluation stage from October 1992 to September 1993. Then, for the IBM analysis, the in-sample phase is from January 1990 to May 1999 and the out-of-sample phase, from June 1999 to May 2000. They assess each model in terms on loss function, as they do not know surely which one is more proper, they suggest six different functions, just in order to observe the power of the models in forecasting future volatility.
Hansen and Lunde, in line with Andersen and Bollerslev, assess the conditional variance by the realized variance and not by the squared return. They do so, because the realized variance or...