Jeff Fleming

Implied volatility functions: Empirical tests

Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) hypothesize that asset return volatility is a deterministic function of asset price and time, and develop a deterministic volatility function (DVF) option valuation model that has the potential of fitting the observed cross section of option prices exactly. Using S&P 500 options from June 1988 through December 1993, we examine the predictive and hedging performance of the DVF option valuation model and find it is no better than an ad hoc procedure that merely smooths Black-Scholes (1973) implied volatilities across exercise prices and times to expiration. Copyright The American Finance Association 1998.

The Economic Value of Volatility Timing Using 'Realized' Volatility

Recent work suggests that intradaily returns can be used to construct estimates of daily return volatility that are more precise than those constructed using daily returns. We measure the economic value of this “realized” volatility approach in the context of investment decisions. Our results indicate that the value of switching from daily to intradaily returns to estimate the conditional covariance matix can be substantial. We estimate that a risk-averse investor would be willing to pay 50 to 200 basis points per year to capture the observed gains in portfolio performance. Moreover, these gains are robust to transaction costs, estimation risk regarding expected returns, and the performance measurement horizon. JEL classification: G11, G14

The quality of market volatility forecasts implied by S&P 100 index option prices

Abstract This study examines the performance of the S&P 100 implied volatility as a forecast of future stock market volatility. The results indicate that the implied volatility is an upward biased forecast, but also that it contains relevant information regarding future volatility. The implied volatility dominates the historical volatility rate in terms of ex ante forecasting power, and its forecast error is orthogonal to parameters frequently linked to conditional volatility, including those employed in various ARCH specifications. These findings suggest that a linear model which corrects for the implied volatilitys bias can provide a useful market-based estimator of conditional volatility.

Trading Costs and the Relative Rates of Price Discovery in Stock, Futures, and Option Markets

In frictionless and rational markets, perfect substitutes must have the same price. In markets with trading costs, however, price differences may be as large as the costs of executing the arbitrage between markets. Moreover, if trading costs differ, trading activity will tend to be concentrated in the lowest-cost market. This study tests the differential trading cost hypothesis by examining the rate at which new information is incorporated in stock, index futures, and index option prices. The lead/lag return relations among markets are consistent with their relative trading costs. Prices in the index derivative markets appear to lead prices in the stock market. At the same time, index futures prices tend to lead index option prices, and the prices of index calls and index puts move together. The trading cost hypothesis reconciles the disparity found between the temporal relation in the stock index/index derivative markets versus the stock/stock option markets.

Implied volatility functions: empirical tests

Black and Scholes (1973) implied volatilities tend to be systematically related to the options exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black/Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying assets return is a deterministic function of the asset price and time and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S and P 500 index options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DVF option valuation model.

The impact of energy derivatives on the crude oil market

We examine the effects of energy derivatives trading on the crude oil market. There is a common public and regulatory perception that derivative securities increase volatility and can have a destabilizing effect on the underlying market. Consistent with this view, we find an abnormal increase in volatility for three consecutive weeks following the introduction of NYMEX crude oil futures. While there is also evidence of a longer-term volatility increase, this is likely due to exogenous factors, such as the continuing deregulation of the energy markets. Subsequent introductions of crude oil options and derivatives on other energy commodities have no effect on crude oil volatility. We also examine the effects of derivatives trading on the depth and liquidity of the crude oil market. This analysis reveals a strong inverse relation between the open interest in crude oil futures and spot market volatility. Specifically, when open interest is greater, the volatility shock associated with a given unexpected increase in volume is much smaller.

Stochastic Volatility, Trading Volume, and the Daily Flow of Information

We use state-space methods to investigate the relation between volume, volatility, and ARCH effects within a mixture of distributions hypothesis (MDH) framework. Most recent studies of the MDH fit AR(1) specifications that require the information flow to be highly persistent. Using a more general specification, we find evidence of a large nonpersistent component of volatility that is closely related to the contemporaneous nonpersistent component of volume. However, in contrast to studies that fit volume-augmented GARCH models, we find no evidence that volume subsumes ARCH effects. Since volume-augmented GARCH models are subject to simultaneity bias, our findings should be more robust than these prior results.

Long Memory in Volatility and Trading Volume

We use fractionally-integrated time-series models to investigate the joint dynamics of equity trading volume and volatility. Bollerslev and Jubinski (1999) show that volume and volatility have a similar degree of fractional integration, and they argue that this evidence supports a long-run view of the mixture-of-distributions hypothesis. We examine this issue using more precise volatility estimates obtained using high-frequency returns (i.e., realized volatilities). Our results indicate that volume and volatility both display long memory, but we can reject the hypothesis that the two series share a common order of fractional integration for a fifth of the firms in our sample. Moreover, we find a strong correlation between the innovations to volume and volatility, which suggests that trading volume can be used to obtain more precise estimates of daily volatility for cases in which high-frequency returns are unavailable.

Component-Driven Regime-Switching Volatility

We develop a new class of regime-switching volatility models that are characterized by high-dimensional state spaces, parsimonious transition matrices, and ARMA dynamics for the log volatility process. This combination of features is achieved by assuming that we can decompose the Markov chain that describes regime dynamics into a number of two-state component chains that evolve independently through time. Using daily data for S&P 500 index and IBM shares, we show that our component-driven regime-switching (CDRS) models are capable of outperforming GARCH, component GARCH, regime-switching GARCH, and Markov-switching multifractal models in forecasting realized variances out of sample. Interestingly, we find that CDRS models with simple AR(1) dynamics perform well across the board. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

ARCH Effects and Trading Volume

Studies that fit volume-augmented GARCH models often find support for the hypothesis that trading volume explains ARCH effects in daily stock returns. We show that this finding is due to an unrecognized constraint imposed by the GARCH specification used for the analysis. Using a more flexible specification, we find no evidence that inserting volume into the conditional variance function of the model reduces the importance of lagged squared returns in capturing volatility dynamics. Volume is strongly correlated with contemporaneous return volatility, but the correlation is driven largely by transitory volatility shocks that have little to do with the highly persistent component of volatility captured by standard volatility models.