Alternative Volatility Forecasting Method Evaluation

Alternative Volatility Forecasting Method EvaluationFor many monetary market applications, including substitute(a) pricing and investment decisions, capriciousness apprehending is crucial. Therefore, the research of irritability forecast has been an active ara of study since the one-time(prenominal) years. In recent years, the emergence of many financial time serial methods for irritability forecasting has proved the importance of down the stairsstanding the nature of volatility in any financial instruments.Often, people will think price is use as an power of the fund market performance. Due to the non-stationary nature of price series of the melodic line market, almost researchers actually transformed series of price budge (return) or absolute price changes (absolute return) in their studies. There is a difference between the term return and the term volatility. The term volatility is utilize as a crude measure of the total risk of financial assets. Actually, vol atility is the standard deviation or the random variable of returns whereas return is me desire the changes of prices.An increasingly unremarkably adopted tool for the measurement of the risk exposure associated with a particular portfolio of assets cognize as Value at Risk (var) involves calculation of the expected losses that might solution from changes in the market prices of particular securities (Jorion, 2001 Bessis, 2002). Thus, the VaR of a particular portfolio is defined as the maximum loss on a portfolio occurring in spite of appearance a specified time and with a habituated (small) probability. Under this approach, the validity of a banks internally idealed VaR is backtested by comparing actual day by day trading gains or losses with the estimated VaR and noting the number of exceptions occurring, in the sense of days when the VaR estimate was insufficient to cover actual trading losses, with concerns course arising where such exceptions frequently occur, and that can result in a range of penalties for the financial institution concerned (Sa chthonics Cornett, 2003).A crucial parameter in the death penalty of parametric VaR calculation methods is an estimate of the volatility parameter that describes the asset or portfolio, or more accurately a forecast of that volatility where the simplifying speculation of constancy is relaxed and time-varying volatility is acknowledged. While it has long been recognized that returns volatility exhibits clustering, such that large (small) returns follow large (small) returns of random sign (Mandelbrot, 1963 Fama, 1965), it is only following the introduction of the generalized autoregressive conditional heteroskedasticity (GARCH) model (Engle, 1982 Bollerslev, 1986) that financial economists have modeled and forecast these temporal dependencies development econometric techniques, and a variety of adaptations of the basic GARCH framework ar now widely use in modeling time-varying volatility. In particu lar, the significance of asymmetric effects in stock index returns has been widely documented, such that candor return volatility increases by a greater amount following positive shocks, usually associated with the leverage effect, whereby a firms debt-to- truth ratio increases when equity comforts decline, and holders of that equity perceive future income streams of the firm as being more risky (Black, 1976 Christie, 1982). Such magnetic variation asymmetry has been successfully modeled and forecast in a variety of market contexts (Henry, 1998) apply the threshold-GARCH (TGARCH) model (Glosten et al., 1993), and the exponential function-GARCH (EGARCH) model (Nelson, 1991) in particular.Problem StatementWhile risk management practises in financial institutions often rely on unanalyzabler volatility forecasting approaches based on heuristics and moving average, smoothing or RiskMetrics techniques, symmetric and asymmetric GARCH models have alike recently begun to be considere d in the VaR context. However, the standard GARCH model and variants within that class of model impose rapid exponential decay in the effect of shocks on conditional version. In contrast, observational evidence has suggested that volatility tends to change slowly and that shocks take a considerable time to decay (Ding et al., 1993). The fractionally integrated-GARCH (FIGARCH) model (Baillie et al., 1996 Chung, 1999) has wind a popular means of capturing and forecasting such non-integrated but highly persistent long remembering dynamics in volatility in the recent empirical literature, as well as its exponential (FIEGARCH) variant (Bollerslev Mikkelsen, 1996) which parallels the EGARCH extension of the basic GARCH form, and therefore provides a generalization capable of capturing both the volatility asymmetry and long memory in volatility which be potential characteristics of emerging equity markets.Research ObjectivesThis paper therefore seeks to extend preliminary research c oncerned with the evaluation of alternative volatility forecasting methods under VaR modeling in the context of the Basle Committee criterion for determining the adequacy of the resulting VaR estimates in two ways. First, by broadening the class of GARCH models under consideration to include more recently proposed models such as the FIGARCH and FIEGARCH representations described above, which argon capable of accommodating potential fractional integration and the associated long memory characteristics of return volatility, as well as the more simplistic and computationally less intensive methods commonly used in financial institutions. Second, extending the scope of previous research through evaluative application of these methods to mundane index entropy of nine stock market indexes.Significance of this studyThe extensive research of volatility forecasting plays an important role for investment, financial risk management, security valuation, and also business decision-making proc ess. Without a proper forecasting tools and research on this field, many financial decision making process will be difficult and risky to be implemented. The positive contribution of volatility forecasting in the field of pay is no doubt a fact as it given many practitioners a mean of guidelines to estimate their management risk such as option pricing, hedging and estimating investment risk.Therefore, it is crucial to study on the performance of opposite approaches and methods of forecast model to determine the best suitable practical application for divers(prenominal) situation. The most common form of financial instrument is the stock market. The stock indices consist of a particular countrys most prominent stocks. Thus, in this study our forecast is to focus on forecasting the stock indices volatility of eight different stock indices that provide us the ability to test the forecast approaches.There are quite a number of forecast models since the recent years. However, the new concern is on the performance of these forecast model when incorporated with higher absolute frequence info with the agnise volatility method. There are still gap for researching the intra-day selective information effects on forecasting model which is comparative new as compared to casual data volatility forecasting. The significant role of this study also include whether intra-day data can really help at improving the performance of forecast model to estimate volatility for the stock index.Review of ChaptersIn this proposal, the report is mainly subdivided into three chapters. Chapter 1 is about the overview of this research which includes the background of the study, the research objective, fuss statement, and the significance of this study. Chapter 2 presents the literature review of volatility forecasting, GARCH models, exponentially smoothing and realized volatility.CHAPTER 2 LITERATURE REVIEW2.1 Volatility forecastingVolatility forecasts are produced by either market-ba sed or time-series methods. Market-based forecasting involves the calculation of implied volatility from current option prices by solving the Black and Scholes option pricing model for the volatility that results in a price equal to the market price. In this paper, our focus is on the development of a new time series method. These methods provide estimates of the conditional variance, 2t = var(rt It-1), of the record return, rt, at time t conditional on It 1, the information set of all observed returns up to time t 1. This can be viewed as the variance of an error (or residual) term, t, defined by t = rt E(rt It 1 ), where E(rt It 1 ) is a conditional mean term, which is often assumed to be zero or a constant. t is often referred to as the price shock? or news?.2.2 Overview of standard volatility forecast model2.2.1 GARCH modelGARCH models (Engle, 1982 Bollersle, 1986) are the most widely used statistical models for volatility. GARCH models express the conditional variance as a linear function of lagged shape error terms and lagged conditional variance terms. For example, the GARCH(1, 1) model is shown in the following expression2t = + 2t 1 + 2t 1,where , , and are parameters. The multiperiod variance forecast, , is calculated as the sum of the variance forecasts for each of the k periods making up the holding periodwhere is the one-step-ahead variance forecast. Empirical results for the GARCH(1, 1) model have shown that often (1 ). The model in which = (1 ) is term integrated GARCH (IGARCH) (Nelson, 1990). exponential function smoothing has the same grammatical construction as the IGARCH(1, 1) model with the additional restriction that = 0. The IGARCH(1, 1) multiperiod forecast is written asStock return volatility is often found to be greater following a negative return than a positive return of equal size. This leverage effect has promted the development of a number of GARCH models that allow for asymmetry. The first asymmetric formulati on was the exponential GARCH model of Nelson (1991). In this log formulation for volatility, the impact of lagged shape residuals is exponential, which may exaggerate the impact of large shocks. A simpler asymmetric model is the GJRGARCH model of Glosten et al. (1993). The GJRGARCH(1, 1) model is given by,where , , , and are parameters and I. is the indicator function. Typically, it is found that , which indicates the presence of the leverage effect. The assumption that the median of the distribution of t is zero implies that the expectation of the indicator function is 0.5, which enables the derivation of the following multiperiod forecast expressionGARCH parameters are estimated by maximum likelihood, which requires the assumption that the standardized errors, t / t, are independent and identically distributed (i.i.d.). Although a Gaussian assumption is common, the distribution is often fat tailed, which has prompted the use of the Student-t distribution (Bollerslev, 1987) and the generalized error distribution (Nelson, 1991).Stochastic volatility models provide an alternative statistical volatility modelling approach (Ghysels et al., 1996). However, estimation of these models has proved difficult and, consequently, they are not as widely used as GARCH models. Andersen et al. (2003) show how nonchalant transfigure rate volatility can be forecasted by fitting long-memory, or fractionally integrated, autoregressive and vector autoregressive models to the log realized day by day volatility constructed from half-hourly returns. Although results for this approach are impressive, such high frequency data are not available to many forecasters, so there is still great interest in methods apply to everyday data. A useful review of the volatility forecasting literature is provided by Poon and Granger (2003).2.2.2 Exponentially SmoothingExponentially heavy Moving Average (EWMA) is simple and well-known volatility forecast method. The method is based on the si mple average of past square residuals to estimate its variance forecasts. The EWMA allows the latest observations to have a stronger weighted impact on the volatility forecast of past data observations. The equivalence for the EWMA is shown and written as exponential smoothing in recursive form. The parameter is the smoothing parameter.The parThere is no proper guideline or statistic model for exponential smoothing. Generally, literature suggested using reduction in the sum of in-sample one-step-ahead estimation of errors (Taylor, 2004 cited from Gardner, 1985). In RiskMetrics (1996), volatility forecasting for exponential smoothing is recommended to use the following minimisationIn the above equation, 2t is the in-sample form error which acted as the proxy foractual variance whereby it is express to be not observable. By using 2t as a proxy forvariance, the actual squared residual, 2t, is said to be biased and noisy. In Andersenet al. (1998), the research showed the evaluation of variance forecasts using bring in volatility as a more accurate proxy. The next section would discuss more on the literature of realised volatility. The work of high frequency data for realised volatility in forecast evaluation can be applied in parameter estimation for exponential smoothing with the following minimisation expression.2.2.3 Realised volatilityThe recent researchs interest in using a comparative volatility estimator as an alternative has emerged a significant literatures on volatility models that incorporated high frequency data. One of the emerging theories for a comparative volatility estimator is the so called agnise Volatility. Realized volatility is referred as the volatility calculated using a short period time series or using higher frequency periods. In Andersen and Bollerslev (1998) showed that high frequency data can be used to compute daily realize volatility which showed a better true variance than the usual daily return variance. This concept is ad opted in Andersen, Bollerslev, Diebold Labys (2003) to forecast the daily stock volatility which found that the additional intraday information are provide better result in forecasting low volume and up market day.The application of realized volatility has also been occupied by Taylor (2004) in parameters estimation for weekly volatility forecasting using realised volatility derived from daily data. An encouraging result were showed by using the smooth transition exponential smoothing method whereby the research used eight stock indices to compare the weekly volatility forecast of this method with other GARCH models (Taylor, 2004). The concept of realized volatility has been employed by many researchers in forecasting of many other financial assets such as foreign exchange rates, individual stocks, stock indices and etcetera.One of the primordial application of realized volatility concept has used spot exchange rates of Deutschemark-US dollar and Japanese Yen-US dollar to show th e superiority of using intraday data as realized volatility measure. The sum of squared five-minute high frequency returns incorporated in the forecasting model proved to outperform the daily squared returns as a volatility measure (Andersen et al., 1998). Another similar study done by Martens (2001) has adopted realized volatility in forecasting daily exchange rate volatility using intraday returns. The results showed that using highest available frequency of intraday returns leads to superior daily volatility forecast.Furthermore, realized volatility approach has also been blanket(a) to studies for risk and return trade-off using high frequency data. In Bali et al. (2005), the research provided strong positive correlation between risk and return for stock market using high frequency data. The usage of daily realized which incorporated valuable information from intraday returns produce more accurate measure of market risk. In addition to this study, Tzang et al. (2009) as applied the realized volatility approach as a proxy for market volatility rather than squared daily returns to assess the efficiency of various model based volatility forecast.Finally, the findings from a research done by Andersen, Bollerslev, Diebold Labys (2001) shown that realized volatility in certain conditions is costless for measurement error and unbiased estimator for return volatility. The proven research has prompted many recent works in forecasting intra-day volatility to applied realized volatility for their studies. This can be observed in McMillan Garcia (2009), Fuertes et al. (2009), Frijns et al.(2008) and Martens (2001). Many researchers exploit the advantage of realised volatility as an unbiased estimators measure for intra-day data and also as a simplified way to incorporated additional information into other forecast models.McMillan et al. (2009) utilised realised volatility to capture intraday volatilities itself as fence to most researchers that uses realised volat ility for daily realised approach. The study showed Hyperbolic Generalized Autoregressive Conditional Heteroscedasity (HYGARCH) as the best forecast model of intra-day volatility.2.3 Forecast Models used in this studyThe forecast models that are presented in this study includeRandom Walk (RW)30 days Moving Average (MA30)Exponentially Weighted Moving Average (EWMA) with =0.06 (RiskMetrics)Exponentially Smoothing with optimised (ES)Integrated General Autoregressive Conditional Heteroskedastic using daily data (IGARCH)Exponentially Weighted Moving Average (Riskmetrics) on daily realised volatility calculated from intraday data. (EWMA-RV)Exponentially Smoothing with optimised on daily realised volatility calculated from intraday data. (ES-RV)General Autoregressive Conditional Heteroskedasticity model with intraday data using realised volatility approach (INTRAGARCH)Integrated General Autoregressive Conditional Heteroskedasticity with intraday data using realised volatility approach (I GARCH)General Autoregressive Conditional Heteroskedasticity with daily realised volatility (RV-GARCH)CHAPTER 3 DATA AND METHODOLOGY3.1 Sample selection and description of the studyVarious comparative forecast models are used in order to value the performance of incorporating intraday data. This study used dataset from nine stock indices include Malaysia (FTSE-BMKLCI), Singapore (STI), Frankfurt-Germany (DAX30), Hong Kong (Hang Seng Index), London-United Kingdom (FTSE100), France (CAC40), Shanghai-China (SSE), Shenzhen-China (SZSE), and United States (SP 100). These series consisted of daily closing prices and also the intraday hourly cultivation price of their respective indices.The daily closing prices were retrieved using DataStream Advance 4.0? and also from Yahoo Finance (http//finance.yahoo.com). Whereas, the hourly intraday last prices of these stock indices were retrieved from Bloomberg Terminal from Bursa Malaysia. Each stock index has their respective trading hours last pr ice which produced a different number of observations for each series. The total number of trading hours within the day differed among different stock index.However, the sample period used in this study spanned approximately for 300 trading days, from 15 October 2009 to 15 March 2011. In order to simplify the study, the focus is based on a one-step-ahead volatility forecast. The first 200 trading days log returns were applied to estimate the parameters for various forecast models which is known as the in-sample forecast. The remaining 100 trading days log returns were used for post-sample evaluation. This study aimed to forecast volatility in daily log returns for various forecasting methods and used daily realised volatility as proxy for actual volatility. The next subsections presented the data description and the 10 forecast methods which will be considered in the study.3.2 Data Analysis3.2.1 Forecasting MethodsThis subsection describes the methodology to forecast the in-sample a nd out-sample performance of various forecast models. The forecast model includes Random Walk (RW), Moving Average, GARCH models, and Exponential smoothing techniques.3.2.1.1 Standard volatility forecast model using daily returnsThis project paper adopted the simple moving average of squared residuals from the recent past 30 daily observations which is labelled as MA30 and the Random Walk (RW) for the standard volatility forecast model as performance benchmark. The 30 day simple moving average is given byWhereby, 2 = (rt )2 shown in the previous section. The moving average is able to smooth out the short running fluctuations and strain on the long run trends or cycles through a series of averaging different subsets of datasets.On the other hand, the Random Walk (RW) is explained as the forecast result is equal to the actual value of the recent period. The actual value in this study used is the squared residual denoted as, 2t. The equation is as shown below?Tomorrows forecasted val ue = yesterday actual value ()3.2.1.2 GARCH models for hourly and daily returnsThere are many different GARCH models for forecasting volatility that can be included in this research. However, the consideration in this study is limited to 2 forecast GARCH models which are the GARCH and IGARCH for practicality. The GARCH models in this study have applied GARCH (1, 1) specifications. The three forecast model used were labelled as IGARCH, INTRA-IGARCH, and INTRA-GARCH models.The IGARCH model is estimated using daily residuals as daily data is easily obtained from the source mentioned above. The general IGARCH forecast model used is given by?? ?But, the parameter estimate generate by EVIEW 7 will be using the following expression? ? ?? ?However, the INTRA-IGARCH and INTRA-GARCH models used hourly residual data to estimate the forecast for daily realised volatility. The forecast for volatility of these models over an N-trading hours span period would be recognised as the forecast of daily volatility. The N trading hours span period is dependent on the trading hours of a specified stock index. In order to calculate the daily realised volatility, the equation is for N trading hours in a day for a particular stock index is given byWhere period i is the higher frequency of hourly data and the 2t, is the squared residual of the particular hour. For example, if KLCI index has a 7 trading hours per day, the realised daily volatility is calculated from the sum of squared residual of these 7 hours. Additionally, forecast models such as INTRA-IGARCHand INTRA-GARCH applied equation 3 to obtain the daily realised volatility by replacing the squared residual, 2t with values that is forecasted using these models.3.2.1.3 GARCH model using realised volatilityThe GARCH model can be estimated using daily realised volatility which isderived from the hourly squared residual with equation 3. In order to apply RV forGARCH forecast model, equation 3 has to be modified to be squared root t o be ableto obtain the parameter estimates that is needed using EVIEW 6. The equation is asfollowAs for this project paper, the GARCH model that used daily realised volatility asinput data is labelled as RV-GARCH.3.2.1.4 Exponential smoothing and EWMA methodsThe forecast model for exponential smoothing method has been implementedinto two approaches. The first is by using minimisation of equation 3 to optimise theparameter and it is labelled as ES for this project paper. The actual value (squaredresidual), 2t is obtained from the daily data. The second approach which is said to bethe better proxy variance forecast has applied equation 4 for the minimisation. Theforecast model for this exponential smoothing method is termed as ES-RV whichadopted daily realised volatility from hourly data.Apart from that, the study also considered the smoothing parameter as a fixed value of 0.06 as recommended by RiskMetrics (1996) for model using daily data and daily realised volatility data derived from hourly data. The forecast model is termed as EWMA and EWMA-RV respectively. By using equation 2 as shown previously, the EWMA used daily squared residual as 2t 1 parameter input while the EWMA-RV used the daily realised volatility as the 2t 1 parameter input.3.3 Research Design (Gantt Chart)JulAugSepOctNovDecJanFebMarLiterature ReviewMethodologyResearch proposalData collectionData analysisDiscussion and conclusion