# Comparing the accuracy of the volatility forecasting models, GARCH, SV and EWMA under different scenarios

# Introduction

Because of the rapid development of new and complex financial instruments in financial markets, the forecasting volatility of assets is playing a central role on risk management tasks and evaluating asset in finance. However, interestingly, the ability of forecasting accuracy of stochastic volatility always catches people’s eyes, because nobody wants loss his/her profits by inaccurate predictions. Opportunities might be lost due to overestimating of volatility; investors bear risk due to underestimating of volatility. In addition, risk control strategies and profitable portfolio are deeply influenced by accuracy of volatility forecasting models. After the financial crisis happened in 2008, generally, investors concentrate on risk-free investment rather than a risk one. Therefore, my paper is going to examine three different models, GARCH (see, for example, Bollerslev (1986)), SV (Taylor, 1986) and EWMA (see McAleer (2005)), under diverse volatility scenarios. By using those volatility models, a simulation experiment will take a wide series of volatility scenarios representatives, which are typical in financial market or real assets market, to test their rates of return separately.

My dissertation is consisted of 5 chapters including the introduction, literature review, methodology and empirical research, as well as the conclusion. Different chapters focus on different key points, but there are tight relationships within each other and they are constructed as follows.

The introduction presents my personal ideas and understanding of fundamental concepts about negative relation between investment return and volatility, as well as three volatility forecasting models mentioned above. Generally, Generalised Autoregressive Conditional Heteroscedasticity (GARCH) and Stochastic Volatility (SV) are main two forecasting volatility methodology, nonetheless, considering the diversification of data source would have different effects on different models, it would be better to employ other forecasting volatility model, like EWMA model, to perform the simulation experiment which makes my results more convincing.

Employing other people’s ideas of forecasting volatility from journals and papers, literature review will provide the historical developments of volatility forecasting models in asset markets. Simultaneously, several sparking ideas will be explained with the frame work of previous approaches of volatility forecasting models. Moreover, the problems founded in previous researches can also be avoided. For example, the inherent problem of the conditional variance indirect observed in using models measuring volatility, GARCH family models, SV models or EWMA have been advocated widely in literatures related (Michael, M. (2010)). Fundamentally, the journal of *Autoregressive Conditional Heteroscedasticity with Estimated of the Variance of United Kingdom Inflation* illustrated the frame work of ARCH model (Engle (1982)) that helps us deepen understanding of negative correlation between stock return and volatility, as well as the basic frame of forecasting volatility model. Other academic journals, like *Answering the sceptics:Yes, standard volatility models do provide accurate forecasts *(Andersen, T. & Bollerslev, T. (1988)), *ARCH modelling in finance: a review of the theory and empirical evidence* (Bollerslev, T. Chou, R. & Kroner, K (1992)), *Return to RiskMetrics: The Evolution of a Standard* (RiskMetrics Group, Inc. (2001)), *Forecasting accuracy of stochastic volatility, GARCH and EWMA models under different volatility scenarios* (Nigel, M & D. Jie (2010)), which provides strong fundamental theoretical evidences, will be referred to my dissertation and support my original hypothesis accuracy comparison of three different volatility forecasting models in the dissertation. From those academic journals or papers with different approaches with volatility forecasting models, some drawbacks of models can be modified. For instance, as observed by Bollerslev, T. (1987), several stylized facts cannot be predicted precisely by a majority of the latent volatility models. Nonetheless, those factors can be caught effortlessly on financial time series.

The methodology discusses briefly empirical demonstration of GARCH, SV and EMWA models separately, including notations and data sources, the results of simulation experiment will also be shown in this section. As mentioned by Nigel(2010), “ for the simulated data, we contrast the accuracy of volatility estimated in-sample and out-of sample using a range of error measures.” Besides, another critical point is to make suitable definition of the volatility space according to three different volatility forecasting models with a triplet of coefficients, for instance, CV^{2}_{garch }is determined by coefficients (). Afterwards, applying the process of realized variance, 100 examples of length=500, 1000, 3000 will be generated corresponding to each parameters. Utilizing 100 examples with T=1100 realization, an SV model, a GARCH model and an EWMA model are used to assess volatility with the decay factor suggested (RiskMetrics, 2001). The front 1000 data points are used for in-sample forecasting, while the remainder is served as out-of-sample estimation. In order to achieve effectively comparison within three models with observed and estimated volatilities (Brailsford and Faff, 1996), three measures of forecasting accuracy are used (RMSE, MME(U),MME(0)).

Empirical research section illustrates the findings employing real data source, which is consisted of 16 financial data sets. The data source is comprised of four equities, four commodities, four FX series and four equity indexes. All data are collected between 1 January 2000 and 31 December 2010 from data-stream. With difference logarithms of consecutive closing prices, the rates of return of different assets are figured out. In consideration of covering sufficient volatility scenario as much as possible, therefore, in diversified main financial markets, especially, small number of samples with frequent floating price in asset markets would be included. In addition, cross-section data with capturing examples would be chosen and then examined in the simulation experiment. In a word, the empirical research will present strong evidence, with real-financial data source, to prove the original ideas about accuracy comparison of three volatility forecasting models. Meanwhile, due to the imperfection of data source and the volatility forecasting models, which would affect the results of simulation, some acceptable biased results of the simulation experiments will be explained exhaustively.

The final section (conclusion) will give a succinct summary of the simulation experiments under a series of volatility scenarios defined with persistence and volatility of volatility. Furthermore, unavoidable drawbacks of the simulation experiments will be explained, and feasible improvements will be promoted in this part, as well as bringing up further research about this topic and its trend of development. For example, analysing typical high frequency data with the seasonal changes, the results of accuracy of these three forecasting volatility models would show any empirical change or not.

Reference

Anderson, T.G. and T. Bollerslev (1998) Answering the skeptics: yes, standard volatility models do provide accurate forecasts, *International Economic Review*, 39, 885-905.

Bollerslev, T. (1986) Generalized autoregressive conditional heteroscedasticity, *Journal of Econometrics*, 31,307-27

Bollerslev, T. (1987) A conditionally heteroscedasticity time series model for speculative prices and rates of return, *Review of Economics and Statistics*, **69**, 542 – 547.

Bollerslec, T., R. Chou and K. Kroner (1992) ARCH modeling in finance: a view of the theory and empirical evidence, *Journal of Econometrics*, 52, 2-59

Brailsford, T. and R. Faff (1996) An evaluation of volatility forecasting techniques, *Journal of Banking and Finance*, 20, 419-38

Ding J. and N. Meade (2010), Forecasting accuracy of stochastic volatility, GARCH and EWMA models under different volatility scenarios, Applied Financial Economics, 20, 771-783

Engle, R. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, *Econometrica*, 50, 987-1008

McAleer, M. (2005) Automated inference and learning in modeling financial volatility, *Econometric Theory*, **21**, 232 – 261.

McAleer, M. (2010) *Modelling and Forecasting Noisy Realized Volatility*, Department of Economics and Finance, College of Business and Economics, University of Canterbury

RiskMetrics Group, Inc. (2001) *Return to Risk Metrics: The Evolution of a Standard*, New York

Taylor, S.J. (1986) *Modelling Financial Time Series*, Wiley, Chichester.

**Category**: Finance, Free Essays