Can the evolution of implied volatility be forecasted? Evidence from European and US implied volatility indices

We address the question whether the evolution of implied volatility can be forecasted by studying a number of European and US implied volatility indices. Both point and interval forecasts are formed by alternative model specifications. The statistical and economic significance of these forecasts is examined. The latter is assessed by trading strategies in the recently inaugurated CBOE volatility futures markets. Predictable patterns are detected from a statistical point of view. However, these are not economically significant since no abnormal profits can be attained. Hence, the hypothesis that the volatility futures markets are efficient cannot be rejected.     

Does the weather affect stock market volatility?

This paper investigates the empirical association between stock market volatility and investor mood-proxies related to the weather (cloudiness, temperature and precipitation) and the environment (nighttime length). Overall, our results suggest that cloudiness and length of nighttime are inversely related to historical, implied and realized measures of volatility. The strength of association seems to vary with the location of an exchange on Earth with respect to the equator. Weather deviations from seasonal norms and dummies representing extreme weather conditions do not offer additional explanatory power in our datasets.     

Lévy processes driven by stochastic volatility

In this paper we extend option pricing under Lévy dynamics, by assuming that the volatility of the Lévy process is stochastic. We, therefore, develop the analog of the standard stochastic volatility models, when the underlying process is not a standard (unit variance) Brownian motion, but rather a standardized Lévy process. We present a methodology that allows one to compute option prices, under virtually any set of diffusive dynamics for the parameters of the volatility process. First, we use ‘local consistency’ arguments to approximate the volatility process with a finite, but sufficiently dense Markov chain; we then use this regime switching approximation to efficiently compute option prices using Fourier inversion. A detailed example, based on a generalization of the popular stochastic volatility model of Heston (Rev Financial Stud 6 (1993) 327), is used to illustrate the implementation of the algorithms. Computer code is available at www.theponytail.net/     

Statistical estimation of Lévy-type stochastic volatility models

Volatility clustering and leverage are two of the most prominent stylized features of the dynamics of asset prices. In order to incorporate these features as well as the typical fat-tails of the log return distributions, several types of exponential Lévy models driven by random clocks have been proposed in the literature. These models constitute a viable alternative to the classical stochastic volatility approach based on SDEs driven by Wiener processes. This paper has two main objectives. First, using threshold type estimators based on high-frequency discrete observations of the process, we consider the recovery problem of the underlying random clock of the process. We show consistency of our estimator in the mean-square sense, extending former results in the literature for more general Lévy processes and for irregular sampling schemes. Secondly, we illustrate empirically the estimation of the random clock, the Blumenthal-Geetor index of jump activity, and the spectral Lévy measure of the process using real intraday high-frequency data.     

Misreaction or misspecification? A re-examination of volatility anomalies

Existing research examines the impact of volatility shocks on the relative pricing of long-term vs. short-term options and documents patterns of “short-horizon underreaction” and “long-horizon overreaction” in the options market. These studies, however, rely on implied volatilities derived from specific option-pricing models and are thus subject to model specification errors. In this paper, we show that these anomalous patterns are the result of model misspecification as opposed to market misreaction. We provide evidence that these patterns are consistent with, in both direction and magnitude, inherent biases in the misspecified models. We also apply a model-free approach to re-examine the anomalous patterns and find no evidence of market misreaction.     

Central bank intervention and exchange rate volatility — Australian evidence

This paper examines the key characteristics of foreign exchange intervention by the Reserve Bank of Australia in the period 1983–1997, which can be broken into five distinct phases. We investigate the changing effectiveness of daily intervention on the $US/$A exchange rate by decomposing the exchange rate response to the intervention into various separate components. We find contemporaneous positive correlation between the direction of intervention and the conditional mean and variance of exchange rate returns. We show that sustained and large interventions have a stabilising influence in the foreign exchange market in terms of direction and volatility. Without these interventions, the market would have moved further and exhibited more volatility.     

Calibrating the exponential Ornstein–Uhlenbeck multiscale stochastic volatility model

This paper demonstrates a tractable and efficient way of calibrating a multiscale exponential Ornstein–Uhlenbeck stochastic volatility model including a correlation between the asset return and its volatility. As opposed to many contributions where this correlation is assumed to be null, this framework allows one to describe the leverage effect widely observed in equity markets. The resulting model is non-exponential and driven by a degenerate noise, thus requiring a high level of care in designing the estimation algorithm. The way this difficulty is overcome provides guidelines concerning the development of an estimation algorithm in a non-standard framework. The authors propose using a block-type expectation maximization algorithm along with particle smoothing. This method results in an accurate calibration process able to identify up to three timescale factors. Furthermore, we introduce an intuitive heuristic which can be used to choose the number of factors.     

What drives volatility persistence in the foreign exchange market?

We propose a new empirical specification of volatility that links volatility to the information flow, measured as the order flow in the market, and to the price sensitivity to that information. The time-varying market sensitivity to information is estimated from high-frequency data, and movements in volatility can therefore be directly related to movements in order flow and market sensitivity. Empirically, the model explains a large share of the long-run variation in volatility. Importantly, the time variation in the market's sensitivity to information is at least as relevant in explaining the persistence of volatility as the rate of information arrival itself. This may be evidence of a link between changes over time in the aggregate behavior of market participants and the time-series properties of realized volatility.     

Can the implied volatility surface move by parallel shifts?

This note explores the analogy between the dynamics of the interest rate term structure and the implied volatility surface of a stock. In particular, we prove an impossibility theorem conjectured by Steve Ross.     

Pricing volatility of stock returns with volatile and persistent components

This paper introduces a two-component volatility model based on first moments of both components to describe the dynamics of speculative return volatility. The two components capture the volatile and the persistent part of volatility, respectively. The model is applied to 10 Asia-Pacific stock markets. Their in-mean effects on returns are tested. The empirical results show that the persistent component is much more important for the volatility dynamic process than is the volatile component. However, the volatile component is found to be a significant pricing factor of asset returns for most markets. A positive or risk-premium effect exists between the return and the volatile component, yet the persistent component is not significantly priced for the return dynamic process.

A behavioral explanation for the negative asymmetric return–volatility relation

We examine the short-term dynamic relation between the S&P 500 (Nasdaq 100) index return and changes in implied volatility at both the daily and intraday level. Neither the leverage hypothesis nor the volatility feedback hypothesis adequately explains the results. Alternatively, we propose that the behavior of traders (from the representativeness, affect, and extrapolation bias concepts of behavioral finance) is consistent with our empirical results of a strong daily and intraday negative return–implied volatility relation. Moreover, both the presence and magnitude of the negative relation and the asymmetry between return and implied volatility are most closely associated with extreme changes in the index returns. We also show that the strength of the relation is consistent with the implied volatility skew.     

Can exchange rate volatility explain persistence in the forward premium?

The persistence of the forward premium has been cited both as evidence of the failure of the unbiasedness hypothesis and as rationale for the forward premium anomaly. This paper examines the recent proposition that forward premium persistence can be explained solely by the conditional variance of the spot rate. We provide theoretical and empirical evidence to challenge this proposition. Our empirical results are shown to be robust to the presence of structural breaks. A corollary of the results is that the ‘true’ risk premium contains a long memory component. This is non-standard and has implications for the construction of rational expectations models of the foreign exchange market.     

How to make Dupire’s local volatility work with jumps

There are several (mathematical) reasons why Dupire’s formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note, we attempt to explain why. In particular, we propose a regularization procedure of the option data so that Dupire’s local vol diffusion process recreates the correct option prices, even in manifest presence of jumps.     

Does knowing the volatility states affect the market risk premium?

Mayfield (J Financ Econ 73:465–496, 2004) has devised a method for estimating the market risk premium, based on a variant of Merton’s ICAPM wherein volatility is specified as a two-state Markov process. In this study, we assess Mayfield’s key assumption that investors know the current volatility state with certainty, via empirical testing of the assumption of exogenous Markov-switching in Mayfield’s model. We detect strong evidence of endogenous switching. This indicates that investors infer the current volatility state, as opposed to simply observing it. We also find that the risk premium estimates are affected by the switching type.     

How asymmetric is U.S. stock market volatility?

This paper explores differences in the impact of equally large positive and negative surprise return shocks in the aggregate U.S. stock market on: (1) the volatility predictions of asymmetric time-series models, (2) implied volatility, and (3) realized volatility. Following large negative surprise return shocks, both asymmetric time-series models (such as the EGARCH and GJR models) and implied volatility predict an increase in volatility and, consistent with this, ex post realized volatility normally rises as predicted. Following large positive return shocks, asymmetric time-series models predict an increase in volatility (albeit a much smaller increase than following a negative shock of the same magnitude), but both implied and realized volatilities generally fall sharply. While asymmetric time-series models predict a decline in volatility following near-zero returns, both implied and realized volatility are normally little changed from levels observed prior to the stable market. The reasons for the differences are explored.     

Australia’s equity home bias and real exchange rate volatility

The main purpose of this paper is to consider the effect of real exchange rate volatility on equity investment by Australian investors. Equity investment is of major importance to savers and investors in Australia. Also real exchange rate volatility is an important influence on Australia’s financial integration in the global economy. Analysis of the effect of real exchange rate volatility on Australia’s equity home bias is important since Australian dollar is a commodity currency. There is a close relationship between Australia’s terms of trade and real exchange rate volatility. Home bias is measured on the basis of free float-adjusted market capitalization in recognition of the fact that closely held shares are not available to ordinary investors. Real exchange rate volatility is measured by deviations from purchasing power parity on a bilateral basis between Australia and 35 countries. The cross-border equity investment data over the period 2001–2007 are from International Monetary Fund’s Coordinated Portfolio Investment Survey. Australian investors are found to invest significantly less in a country if the real exchange rate volatility of that country is relatively high (results that are robust to standard control measures and generalized method of moments).     

Does foreign institutional ownership increase return volatility? Evidence from China

This paper investigates the impact of foreign institutional ownership on firm-level stock return volatility in China, based on our study of a sample of 1458 firms between 1998 and 2008. The empirical results show that share ownership by foreign institutions (both financial and non-financial) increases firm-level stock return volatility, even after controlling for a complete ownership structure, firm size, turnover, and leverage, and correcting for potential endogeneity problems. However, the results also show that foreign individual shareholdings reduce volatility. Furthermore, we document a positive relationship between domestic shareholdings (individual, institutional, and governmental) and firm-level stock return volatility. Empirical results with interaction terms show that foreign institutional ownership increases firm-level return volatility by strengthening the positive impact of liquidity on volatility. The volatility reduction effect of foreign individual ownership is attenuated by government ownership suggests a poor governance environment as a result of the involvement of the Chinese government.     

Is stochastic volatility relevant for dynamic portfolio choice under ambiguity?

Literature on dynamic portfolio choice has been finding that volatility risk has low impact on portfolio choice. For example, using long-run US data, Chacko and Viceira [2005. “Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets.” The Review of Financial Studies 18 (4): 1369–1402] found that intertemporal hedging demand (required by investors for protection against adverse changes in volatility) is empirically small even for highly risk-averse investors. We want to assess if this continues to be true in the presence of ambiguity. Adopting robust control and perturbation theory techniques, we study the problem of a long-horizon investor with recursive preferences that faces ambiguity about the stochastic processes that generate the investment opportunity set. We find that ambiguity impacts portfolio choice, with the relevant channel being the return process. Ambiguity about the volatility process is only relevant if, through a specific correlation structure, it also induces ambiguity about the return process. Using the same long-run US data, we find that ambiguity about the return process may be empirically relevant, much more than ambiguity about the volatility process. Anyway, intertemporal hedging demand is still very low: investors are essentially focused on the short-term risk–return characteristics of the risky asset.     

Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty

In diffusion models, a few suitably chosen financial securities allow to complete the market. As a consequence, the efficient allocations of static Arrow–Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow–Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow–Debreu equilibrium allocations are generically unattainable by dynamically trading a few long-lived assets.     

Where are the sources of stock market mispricing and excess volatility?

Using a simple dividend model, we illustrate and synthesize the sources of stock market mispricing and excess volatility based upon two hypotheses—inflation illusion and heterogeneous beliefs. Our theoretical framework posits that equity mispricing arises when investors have subjective expectations about discount rates or dividend growth rates. We then analyze the sources of equity mispricing and market excess volatility under a VAR framework. Empirically, we find that both inflation illusion and heterogeneous beliefs explain equity mispricing. However, heterogeneous beliefs play a more important role in explaining stock mispricing in the long run. We also find that heterogeneous beliefs cause excess volatility, but inflation illusion does not. Therefore, dispersion in investors’ beliefs is a better explanation of stock market mispricing than the investors’ inability to properly discount future cash flows.