Volatility permeates modern financial theories and decision making processes. As such, accurate measures and good forecasts of future volatility are critical for the implementation and evaluation of asset and derivative pricing theories as well as trading and hedging strategies. In response to this, a voluminous literature has emerged for modeling the temporal dependencies in financial market volatility at the daily and lower frequencies using ARCH and stochastic volatility type models. Most of these studies find highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence. Meanwhile, when judged by standard forecast evaluation criteria, based on the squared or absolute returns over daily or longer forecast horizons, standard volatility models provide seemingly poor forecasts. The present paper demonstrates that, contrary to this contention, in empirically realistic situations the models actually produce strikingly accurate interdaily forecasts f...

It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately-- forecast users naturally have a keen interest in monitoring and improving forecast performance. More generally, forecast evaluation figures prominently in many questions in empirical economics and finance, such as: Are expectations rational? (e.g., Keane and Runkle, 1990; Bonham and Cohen, 1995) Are financial markets efficient? (e.g., Fama, 1970, 1991) Do macroeconomic shocks cause agents to revise their forecasts at all horizons, or just at short- and medium-term horizons? (e.g., Campbell and Mankiw, 1987; Cochrane, 1988) Are observed asset returns "too volatile"? (e.g., Shiller, 1979; LeRoy and Porter, 1981) Are asset returns forecastable over long horizons? (e.g., Fama and French, 1988; Mark, 1995)

Statistical loss functions that generally lack economic content are commonly used for evaluating financial volatility forecasts. In this paper, an evaluation framework based on loss functions tailored to a user’s economic interests is proposed. According to these interests, the user specifies the economic events to be forecast, the criterion with which to evaluate these forecasts, and the subsets of the forecasts of particular interest. The volatility forecasts from a model are then transformed into probability forecasts of the relevant events and evaluated using the specified criteria (i.e., a probability scoring rule and calibration tests). An empirical example using exchange rate data illustrates the framework and confirms that the choice of loss function directly affects the forecast evaluation results.

Characterizing asset return dynamics using volatility models is an important part of empirical finance. The existing literature on GARCH models favors some rather complex volatility specifications whose relative performance is usually assessed through their likelihood based on a time-series of asset returns. This paper compares a range of GARCH models along a different dimension, using option prices and returns under the risk-neutral as well as the physical probability measure. We judge the relative performance of various models by evaluating an objective function based on option prices. In contrast with returns-based inference, we find that our option-based objective function favors a relatively parsimonious model. Specifically, when evaluated out-of-sample, our analysis favors a model that besides volatility clustering only allows for a standard leverage effect. JEL Classification: G12

This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to measure ex post latent volatility imply that standard time series models of the conditional variance become variants of an AR-MAX model. We explore nonlinear departures from these linear specifications using a doubly stochastic process under duration-dependent mixing. This process can capture large abrupt changes in the level of volatility, time-varying persistence, and time-varying variance of volatility. The results have implications for forecast precision, hedging, and pricing of derivatives.

: Covariance matrix forecasts of financial asset returns are an important component of current practice in financial risk management. A wide variety of models are available for generating such forecasts. In this paper, we evaluate the relative performance of different covariance matrix forecasts using standard statistical loss functions and a value-at-risk (VaR) framework. Using a foreign exchange portfolio, we find covariance matrix forecasts generated from option prices perform best under statistical loss functions, such as mean-squared error. Within a VaR framework, the relative performance of covariance matrix forecasts depends greatly on the VaR models' distributional assumptions. Of the forecasts examined, simple specifications, such as exponentially-weighted moving averages of past observations, perform best with regard to the magnitude of VaR exceptions and regulatory capital requirements. Our results provide empirical support for the commonly-used VaR models based on simple c...

The general-to-specific (GETS) approach to modelling is widely employed in the modelling of economic series, but less so in financial volatility modelling due to computational complexity when many explanatory variables are involved. This study proposes a simple way of avoiding this problem and undertakes an out-of-sample forecast evaluation of the methodology applied to the modelling of weekly exchange rate volatility. Our findings suggest that GETS specifications are especially valuable in conditional forecasting, since the specification that employs actual values on the uncertain information performs particularly well.

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov.

In this paper, we examine the use of GARCH models, Neural Network Regression (NNR), Recurrent Neural Network (RNN) regression and model combinations for forecasting and trading currency volatility, with an application to the GBP/USD and USD/JPY exchange rates. Both the results of the NNR/RNN models and the model combination results are benchmarked against the simpler GARCH alternative. The idea of developing a nonlinear nonparametric approach to forecast FX volatility, identify mispriced options and subsequently develop a trading strategy based upon this process is intuitively appealing. Using daily data from December 1993 through April 1999, we develop alternative FX volatility forecasting models. These models are then tested out-of-sample over the period April 1999-May 2000, not only in terms of forecasting accuracy, but also in terms of trading efficiency: In order to do so, we apply a realistic volatility trading strategy using FX option straddles once mispriced options have been identified. Allowing for transaction costs, most trading strategies retained produce positive returns. RNN models appear as the best single modelling approach yet, somewhat surprisingly, model combination which has the best overall performance in terms of forecasting accuracy, fails to improve the RNN-based volatility trading results. Another conclusion from our results is that, for the period and currencies considered, the currency option market was inefficient and/or the pricing formulae applied by market participants were inadequate.

by Hydro-Québec. 3 We have benefited from the useful commentsof Jean-Hugues Lafleur. All remaining errors are our responsibility. This study empirically examines the competitiveness of different forecasting sets of realized volatilities and correlations using linear and nonlinear specifications of time series based on high frequency data. The linear specification uses lagged explanatory variables to explain fractionally integrated series of realized volatilities and correlations. The nonlinear specification consists of a two-step approach. In the first step, joint time series of realized volatilities and correlations are filtered using a multivariate singular system analysis approach. Based on the cleaned series, vectors of nearest neighbors are identified in space and casted into a local linear regression to generate forecasts in the second step. The empirical performance of those specifications is compared to a GARCH diagonal-BEKK model in the context of a trader who would simultaneously quote a call spread option price based on the forecasted parameters and delta-hedge her position with a replicating portfolio. More traditional loss functions based on the absolute forecasting error are also used. The forecasting methodologies based on time series of realized volatilities and correlations generally (but not unanimously) dominate the GARCH approach. Evidence of nonlinearity seems apparent for time series of volatilities irrespective of the return sampling frequency. General performance ranking for the approaches based on realized volatilities and correlations is not robust to the chosen loss function and the return sampling frequency.