[...]... three-month Treasury Bill The model is able to retain the volatility clustering feature of the ARCH model and, in addition, capture the discrete shift in the intercept in the conditional variance that Volatility modelling and forecasting in finance 19 may cause spurious apparent persistence in the variance process The switching-AR(K)Markov-ARCH(G) model of Cai has the following specification: Xt = 0+... properties of the above specification The ARCH-M model was used in asset-pricing theories of CAPM, consumption-based CAPM and the asset-pricing theory of Ross (1976) Depending on the functional form, the conditional mean increases or decreases, with an increase in the conditional variance Mostly linear and logarithmic functions of t2 or t are used in the functional form In the linear specifications, the parameter... existence of ARCH effects in the high-frequency data by the amount of information, or the quality of the information reaching the markets in clusters, or the time between information arrival and the processing of the information by market participants Engle, Ito and Lin (1990a) also suggest information processing as the source of volatility clustering Nelson (1990) shows that the discrete time GARCH(1,1)... for data exhibiting time irreversibility Volatility modelling and forecasting in finance 3 These limitations of ARMA models lead us to models where we can retain the general ARMA framework, allow the WN to be non-Gaussian, or abandon the linearity assumption 1.3 Changes in volatility The main topic of interest of this chapter is the changing volatility found in many time series ARMA models assume a... concentrating on direct forecasting using GARCH, forecasting implied volatility and looking at tick-by-tick data These chapters concentrate much more on theoretical issues in volatility and risk modelling S Bond considers dynamic models of semi-variance, a measure of downside risk G Perez-Quiros and A Timmermann examine connections between volatility of stock markets and business cycle turning points A... forecasting volatility It seems likely that many of these can be incorporated into trading strategies or built into investment technology products The editors have put the book together with the twin goals of encouraging both researchers and practitioners, and we hope that this book is useful to both audiences This page intentionally left blank 1 Volatility modelling and forecasting in finance Linlan... review the methodologies and empirical findings in more than 90 published and working papers that study forecasting performance of various volatility models They also provide recommendations for forecasting in practice, and ideas for further research In this chapter we will briefly review their findings The next section starts with ARMA-type models and discusses their limitations for modelling volatility. .. in the Financial Markets second term on the right-hand side of the equality in (1.17) The analogue of the process dWt in the discrete time specification is zt in (1.12) 1.5.2 Persistence and the SV model In SV models, persistence in volatilities can be captured by specifying a Random Walk (RW) for the ht process Squaring the expression in (1.12) and taking the logarithm of both sides, we obtain: log... (1990b) are other applications in finance Schwert (1989b, 1990) uses the regime switching model to provide a useful descriptive summary of the financial panics during the past century The regime switching model has also been used to model various macroeconomic time series such as the GNP series Explaining business cycles is another application where the recessions are treated as breaks in the time-series... measuring the effect of conditional variance on excess return is interpreted as the coefficient of relative risk aversion In the linear specification, a constant effect of conditional variance on the expected return is hypothesized Harvey (1989), however, reports the coefficient to be varying over time, depending on the phase of the business cycle There is further empirical evidence against the time-invariant . difficulties in running the estimation procedures. With the non- negativity constraint, a shock in the past, regardless of the sign, always has a pos- itive effect on the current volatility: the impact increases. Implementation Computational Finance Linear Factor Models in Finance Initial Public Offerings Funds of Hedge Funds Venture Capital in Europe Series Editor Dr Stephen Satchell Dr Satchell is the Reader in Financial. Tauchen (198 9) explore the daily NYSE value-weighted index for two periods, 1959–1978 and 1954–1984, and find 6 Forecasting Volatility in the Financial Markets significant evidence of ARCH-type conditional