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.     

Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps

The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing high order asymptotic expansions for the at-the-money implied volatility skew, under a rich class of stochastic volatility models with independent stable-like jumps of infinite variation. The case of a pure-jump stable-like Lévy model is also considered under the minimal possible conditions for the resulting expansion to be well defined. Unlike recent results for “near-the-money” option prices and implied volatility, the results herein aid in understanding how the implied volatility smile near expiry is affected by important features of the continuous component, such as the leverage and vol-of-vol parameters. As intermediary results, we obtain high order expansions for at-the-money digital call option prices, which furthermore allow us to infer analogous results for the delta of at-the-money options. Simulation results indicate that our asymptotic expansions give good fits for options with maturities up to one month, underpinning their relevance in practical applications, and an analysis of the implied volatility skew in recent S&P 500 options data shows it to be consistent with the infinite variation jump component of our models.     

Forecasting EUR–USD implied volatility: The case of intraday data

This study models and forecasts the evolution of intraday implied volatility on an underlying EUR–USD exchange rate for a number of maturities. To our knowledge we are the first to employ high frequency data in this context. This allows the construction of forecasting models that can attempt to exploit intraday seasonalities such as overnight effects. Results show that implied volatility is predictable at shorter horizons, within a given day and across the term structure. Moreover, at the conventional daily frequency, intraday seasonality effects can be used to augment the forecasting power of models. The type of inefficiency revealed suggests potentially profitable trading models.     

Why do we smile? On the determinants of the implied volatility function

We report simple regressions and Granger causality tests in order to understand the pattern of implied volatilities across exercise prices. We employ all calls and puts transacted between 16:00 and 16:45 on the Spanish IBEX-35 index from January 1994 to April 1996. Transaction costs, proxied by the bid–ask spread, seem to be a key determinant of the curvature of the volatility smile. Moreover, time to expiration, the uncertainty associated with the market and the relative market momentum are also important variables in explaining the smile.     

Oil prices implied volatility or direction: Which matters more to financial markets?

We examine the impact of oil price uncertainty on US stock returns by industry using the US Oil Fund options implied volatility OVX index and a GJR-GARCH model. We test the effect of the implied volatility of oil on a wide array of domestic industries’ returns using daily data from 2007 to 2016, controlling for a variety of variables such as aggregate market returns, market volatility, exchange rates, interest rates, and inflation expectations. Our main finding is that the implied volatility of oil prices has a consistent and statistically significant negative impact on nine out of the ten industries defined in the Fama and French (J Financ Econ 43:153–193, 1997) 10-industry classification. Oil prices, on the other hand, yield mixed results, with only three industries showing a positive and significant effect, and two industries exhibiting a negative and significant effect. These findings are an indication that the volatility of oil has now surpassed oil prices themselves in terms of influence on financial markets. Furthermore, we show that both oil prices and their volatility have a positive and significant effect on corporate bond credit spreads. Overall, our results indicate that oil price uncertainty increases the risk of future cash flows for goods and services, resulting in negative stock market returns and higher corporate bond credit spreads.     

Market implied future earnings and analysts’ forecasts

This study provides evidence on market implied future earnings based on the residual income valuation (RIV) framework and compares these earnings with analyst earnings forecasts for accuracy (absolute forecast error) and bias (signed forecast error). Prior research shows that current stock price reflects future earnings and that analyst forecasts are biased. Thus, how price-based imputed forecasts compare with analyst forecasts is interesting. Using different cost of capital estimates, we use the price-earnings relation and impute firms’ future annual earnings from three residual income (RI) models for up to 5 years. Relative to I/B/E/S analyst forecasts, imputed forecasts from the RI models are less or no more biased when cost of capital is low (equal to a risk-free rate or slightly higher). Analysts slightly outperform these RI models in terms of accuracy for immediate future (1 or 2) years in the forecast horizon but the opposite is true for more distant future years when cost of capital is low. A regression analysis shows that, in explaining future earnings changes, analyst forecasts relative to imputed forecasts do not impound a significant amount of earnings information embedded in current price. In additional tests, we impute future long-term earnings growth rates and find that they are more accurate and less biased than I/B/E/S analyst long-term earnings growth forecasts. Together, the results suggest that the RIV framework can be used to impute a firm’s future earnings that are high in accuracy and low in bias, especially for distant future years.     

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.     

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.