This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and riskneutral measures are estimated simultaneously. I conclude that the square root stochastic variance model of Heston (1993) and others is incapable of generating realistic returns behavior and find that the data are more accurately represented by a stochastic variance model in the CEV class or a model that allows the price and variance processes to have a time-varying correlation. Specifically, I find that as the level of market variance increases, the volatility of market variance increases rapidly and the correlation between the price and variance processes becomes substantially more negative. The heightened heteroskedasticity in market variance that results generates realistic crash probabilities and dynamics and causes returns to display values of skewness and kurtosis much more consistent with their sample values. While the model dramatically improves the fit of options prices relative to the square root process, it falls short of explaining the implied volatility smile for short-dated options.

Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components and heavy-tailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this paper is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measure-of-fit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated data and daily returns data on the S&P100 index.

Weisbach are gratefully acknowledged. I bear full responsibility for all remaining errors. Forecasting Future Volatility from Option Prices Evidence exists that option prices produce biased forecasts of future volatility across a wide variety of options markets. This paper presents two main results. First, approximately half of the forecasting bias in the S&P 500 index (SPX) options market is eliminated by constructing measures of realized volatility from five minute observations on SPX futures rather than from daily closing SPX levels. Second, much of the remaining forecasting bias is eliminated by employing an option pricing model that permits a non-zero market price of volatility risk. It is widely believed that option prices provide the best forecasts of the future volatility of the assets which underlie them. One reason for this belief is that option prices have the ability to impound all publicly available information – including all information contained in the history of past prices – about the future volatility of the underlying assets. A second related reason is that option pricing theory maintains that if an option prices fails to embody optimal forecasts of the future volatility of the underlying asset, a profitable trading strategy should be available whose implementation would push the option price to the level that reflects the best possible forecast of future volatility.

In 2004 all publications will carry a motif taken from the €100 banknote. This paper can be downloaded without charge from

This article examines the impact of serial correlation in high frequency returns on the realized variance measure. In particular, it is shown that the realized variance measure yields a biased estimate of the conditional return variance when returns are serially correlated. Using 10 years of FTSE-100 minute by minute data we demonstrate that a careful choice of sampling frequency is crucial in avoiding substantial biases. Moreover, we find that the autocovariances of returns disappears under temporal aggregation at a rate of decay that is consistent with an ARMA process under temporal aggregation. A simple autocovariance function based method is proposed for choosing the “optimal ” sampling frequency, that is, the highest available frequency at which the serial correlation of returns has a negligible impact on the realized variance measure. We find that the logarithmic realized variance series of the FTSE-100 index, constructed using an optimal sampling frequency of 25 minutes, can be modelled as an ARFIMA process. Exogenous variables such as lagged returns and contemporaneous trading volume appear to be highly significant regressors and are able to explain a large portion of the variation in daily realized variance.

Option prices can be used to infer the level of uncertainty about future asset prices. The first two parts of this article explain such measures (implied volatility) and how they can differ from the market’s true expectation of uncertainty. The third then estimates the implied volatility of threemonth eurodollar interest rates from 1985 to 2001 and evaluates its ability to predict realized volatility. Implied volatility shows that uncertainty about short-term interest rates has been falling for almost 20 years, as the levels of interest rates and inflation have fallen. And changes in implied volatility are usually coincident with major news about the stock market, the real economy, and monetary policy. Federal Reserve Bank of St. Louis Review, May/June 2005, 87(3), pp. 407-25. Economists often use asset prices along with models of their determination to derive financial markets ’ expectations of events. For example, monetary economists use federal funds futures prices to measure expectations of interest rates (Krueger and Kuttner, 1995; Pakko and Wheelock, 1996). Similarly, a large literature on fixed and target zone exchange rates has used forward exchange rates to measure the credibility of exchange rate regimes or to predict their collapse (Svensson,

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We compare the predictive ability of Stochastic Volatility (SV) models to that of volatility forecasts implied by option prices. An SV model is proposed with implied volatility as an explanatory variable in the variance equation which allows the use of statistical testing; we refer to this model as the SVX model. Next we obtain a Stochastic Implied Volatility (SIV) model by restricting the volatility persistence parameter in the SVX model to equal zero. All SV models are estimated by exact maximum likelihood using Monte Carlo importance sampling methods. The performance of the models is evaluated both within-sample and out-of-sample for daily returns on the Standard & Poor’s 100 index. Our in-sample results confirm the information content of implied volatility measures as the SVX and SIV models produce more effective estimates of the underlying volatility process than the standard SV model based solely on historical returns. The out-of-sample volatility forecasts are evaluated against daily squared returns and intraday volatility measures for forecasting horizons ranging from 1 to 20 days. For both the squared daily returns and the cumulative intraday squared 10-minute returns we find that the SIV model outperforms both the SV and the SVX model on several evaluation criteria but that the SV model produces volatility forecasts with the smallest bias. All models underestimate the volatility process on average which in our opinion is closely related to the fact that the average level of volatility in the estimation samples is lower than in the evaluation sample.

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Abstract: In 2003, the Chicago Board Options Exchange (CBOE) made two key enhancements to the volatility index (VIX) methodology based on S&P options. The new VIX methodology seems to be based on a complicated formula to calculate expected volatility. In this paper, with the use of Thailand’s SET50 Index Options data, we modify the VIX formula to a very simple relationship, which has a higher negative correlation between the VIX for Thailand (TVIX) and SET50 Index Options. We show that TVIX provides more accurate forecasts of option prices than the simple expected volatility (SEV) index, but the SEV index outperforms TVIX in forecasting expected volatility. Therefore, the SEV index would seem to be a superior tool as a hedging diversification tool because of the high negative correlation with the volatility index.