Forecasting volatility Evidence from the German stock market

Forecasting volatility Evidence from the German stock...

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Forecasting Volatility: Evidence from the German Stock Market * Hagen H.W. Bluhm a , Jun Yu b February 2001 Abstract In this paper we compare two basic approaches to forecast volatility in the German stock market. The first approach uses various univariate time series techniques while the second approach makes use of volatility implied in option prices. The time series models include the historical mean model, the exponentially weighted moving average (EWMA) model, four ARCH-type models and a stochastic volatility (SV) model. Based on the utilization of volatility forecasts in option pricing and Value-at-Risk (VaR), various forecast horizons and forecast error measurements are used to assess the ability of volatility forecasts. We show that the model rankings are sensitive to the error measurements as well as the forecast horizons. The result indicates that it is difficult to state which method is the clear winner. However, when option pricing is the primary interest, the SV model and implied volatility should be used. On the other hand, when VaR is the objective, the ARCH-type models are useful. Furthermore, a trading strategy suggests that the time series models are not better than the implied volatility in predicting volatility. JEL classification : G12, G15 Keywords : Forecasting Volatility; ARCH Model; SV Model; Implied Volatility; VaR; Germany * We would like to thank Deutsche Boerse AG, the German stock exchange, for providing the data, and the University of Auckland Research Committee for financial support. a Bankgesellschaft Berlin AG; Email: Hagen.Bluhm@ib.bankgesellschaft.de b Department of Economics, The University of Auckland, Private Bag 92019, Auckland, New Zealand; Email: j.yu@auckland.ac.nz .
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1. Introduction Using daily data from the German stock market, this paper compares two basic approaches to forecast volatility. The first approach uses various univariate time series techniques while the second approach makes use of volatility implied in option prices. The time series models include four ARCH-type models and a stochastic volatility (SV) model. We focus on the forecast horizons of 1, 10, and 180 trading days and 45 calendar days. The evaluation criteria used are mean squared prediction error (MSPE), bounded violations, and the LINEX loss function. A trading strategy is also used to examine the usefulness of the time series models in predicting volatility. Forecasting financial market volatility has received extensive attention in the literature by academicians and practitioners in recent time; see Poon and Granger (2000) (hereafter PG) for an excellent review of the literature. Although “volatility forecasting is a notoriously difficult task” according to Brailsford and Faff (1996) (hereafter BF), it is generally agreed that volatility is predictable and hence the market for volatility is not as efficient as that for returns. Broadly speaking there are two ways to forecast volatility. The first method uses the historical return information only while the second makes use of volatility implied in option prices. The existing empirical evidence is conflicting in three ways. First, within the first method, the performance of
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This note was uploaded on 02/28/2010 for the course ECO 211 taught by Professor Gilo during the Spring '10 term at Young Harris.

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Forecasting volatility Evidence from the German stock...

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