The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets

In this paper we examine the extent of the bias between Black and Scholes (1973)/Black (1976) implied volatility and realized term volatility in the equity and energy markets. Explicitly modeling a market price of volatility risk, we extend previous work by demonstrating that Black-Scholes is an upward-biased predictor of future realized volatility in S&P 500/S&P 100 stock-market indices. Turning to the Black options-on-futures formula, we apply our methodology to options on energy contracts, a market in which crises are characterized by a positive correlation between price-returns and volatilities: After controlling for both term-structure and seasonality effects, our theoretical and empirical findings suggest a similar upward bias in the volatility implied in energy options contracts. We show the bias in both Black-Scholes/Black implied volatilities to be related to a negative market price of volatility risk. JEL Classification G12 · G13     

Global equity market volatilities forecasting: A comparison of leverage effects,jumps, and overnight information

This study extends the HAR-RV model to detailedly compare the role of leverage effects, jumps, and overnight information in predicting the realized volatilities (RV) of 21 international equity indices. First, the in-sample results suggest that these three factors have significantly negative impact for most of international equity markets. Second, the out-of-sample predictive results show that leverage effects and overnight information have stronger predictive power than jumps. Furthermore, we provide convincing results that the use of these three factors simultaneously can produce the best predictions for almost international equity markets at all forecast horizons. Finally, the empirical results from alternative prediction window, Direction-of-Change test, out-of-sample R² test, alternative loss functions, and alternative volatility estimator confirm our results are robust.     

Do bears and bulls swim across oceans? Market information transmission between greater China and the rest of the world

This study investigates returns and volatilities transmission across Greater China’s four emerging stock markets and three developed international markets, Tokyo, London, and New York. Using daily open and close price data from 1994 to 2001, we provide empirical evidence that the overnight returns on all the Greater China stock indices can be estimated by using information from at least one of the three developed markets’ daytime returns. The contemporaneous return spillovers are in general unidirectional from more advanced major international markets to the Chinese markets. However, split-sample analysis suggests that there is also evidence of bi-directional return spillovers after the 1997 Asian financial crisis. We also find that there are no one-period lagged return spillover effects from the three advanced markets to the Chinese markets, except for Taiwan. Finally, Mainland China’s two stock markets are not affected by contemporaneous nor delayed “bad news”.     

Realizing the volatility impacts of sovereign credit ratings information on equity and currency markets: Evidence from the Asian Financial Crisis

We examine the effects of different types of sovereign rating announcements on realized stock and currency market volatilities and cross-asset correlations around periods of financial crises. Using intraday market data and sovereign ratings data for nine sample countries in the Asia-Pacific region over 1997–2001, we find that currency and stock markets react somewhat heterogeneously to various rating announcements and that stock markets are more responsive to rating news than currency markets. We find new evidence that ratings events have significant and asymmetric impacts on intraday market data and that national market attributes influence rating impacts during financial crises.     

Structural breaks in volatility spillovers between international financial markets: Contagion or mere interdependence?

This paper conducts an investigation of volatility transmission between stock markets in Hong Kong, Europe and the United States covering the time period from 2000 up to 2011. Using intra-daily data we compute realized volatility time series for the three markets and employ a Heterogeneous Autoregressive Distributed Lag Model as our baseline econometric specification. Motivated by the presence of various crisis events contained in our sample, we detect time-variation and structural breaks in volatility spillovers. Particularly during the financial crisis of 2007, we find effects consistent with the notion of contagion, suggesting strong and sudden increases in the cross-market synchronization of chronologically succeeding volatilities. Investigating the role of mean breaks and conditional heteroskedasticity in the realized volatilities, however, we find the latter to be the main driver of breaks in volatility spillovers. Taking the volatility of realized volatilities into account, we find no evidence of contagion anymore.     

A note on the importance of overnight information in risk management models

This paper examines the economic value of overnight information to users of risk management models. In addition to the information revealed by overseas markets that trade during the (domestic) overnight period, this paper exploits information generated via recent innovations in the structure of financial markets. In particular, certain securities (and associated derivative products) can now be traded at any time over a 24-h period. As such, it is now possible to make use of information generated by trading, in (almost) identical securities, during the overnight period. Of the securities that are available over such time periods, S&P 500 related products are by far the most actively traded and are, therefore, the subject of this paper. Using a variety of conditional volatility models that allow time-dependent information flow within (and across) three different S&P 500 markets, the results show that overnight information flow has a significant impact on the conditional volatility of daytime traded S&P 500 securities. Moreover (time-consistent) forecasts from models that incorporate overnight information are shown to have economic value to risk managers. In particular, Value-at-Risk (VaR) models based on these conditional volatility models are shown to be more accurate than VaR models that ignore overnight information.     

The Lead‐Lag Relationship Between Cash and Stock Index Futures in a New Market

This paper investigates the lead‐lag relationship in daily returns and volatilities between price movements of the FTSE/ATHEX‐20 and FTSE/ATHEX Mid‐40 stock index futures and the underlying cash indices in the relatively new futures market of Greece. Empirical results show that there is a bi‐directional relationship between cash and futures prices. However, futures lead the cash index returns, by responding more rapidly to economic events than stock prices. This speed is much higher in the more liquid FTSE/ATHEX‐20 market. Moreover, results indicate that futures volatilities spill information over to the corresponding cash market volatilities in both investigated futures markets, but volatilities in the cash markets have no effect on the volatilities of futures markets. Overall, it seems that new market information is disseminated faster in the futures market compared to the stock market. This implies that the futures markets can be used as price discovery vehicles, providing further evidence that derivatives markets contribute to completing and stabilising capital markets in Greece. A further finding of this study is that futures volume and disequilibrium effects between cash and futures prices are important variables in the explanation of volatilities in cash and futures markets.     

A leader of the world commodity futures markets in the making? The case of China's commodity futures

We use the daily data of 16 commodity futures contracts traded in China and corresponding foreign markets (the US, the UK, Japan, and Malaysia) to analyze the linkages between markets. Several findings are noteworthy. First, trading returns of foreign markets, such as the US, have significant impact on China's overnight (close-to-open) returns and vice-versa. Second, daytime (open-to-close) returns of many Chinese commodity futures contracts are not led by foreign daytime returns. Finally, the close-to-close returns analysis suggests that there are no significant lead-lag relationships between the Chinese and foreign markets. These results suggest that (1) the Chinese commodity futures markets are information-efficient, and (2) they are likely to be driven by local market dynamics occurring during the daytime trading session.     

Realizing the volatility impacts of sovereign credit ratings information on equity and currency markets: Evidence from the Asian Financial Crisis

We examine the effects of different types of sovereign rating announcements on realized stock and currency market volatilities and cross-asset correlations around periods of financial crises. Using intraday market data and sovereign ratings data for nine sample countries in the Asia-Pacific region over 1997–2001, we find that currency and stock markets react somewhat heterogeneously to various rating announcements and that stock markets are more responsive to rating news than currency markets. We find new evidence that ratings events have significant and asymmetric impacts on intraday market data and that national market attributes influence rating impacts during financial crises.     

Volatility dependences of stock markets with structural breaks

We develop a Vector Heterogeneous Autoregression model with Continuous Volatility and Jumps (VHARCJ) where residuals follow a flexible dynamic heterogeneous covariance structure. We employ the Bayesian data augmentation approach to match the realised volatility series based on high-frequency data from six stock markets. The structural breaks in the covariance are captured by an exogenous stochastic component that follows a three-state Markov regime-switching process. We find that the stock markets have higher volatility dependence during turmoil periods and that breakdowns in volatility dependence can be attributed to the increase in market volatilities. We also find positive correlations between the Asian stock markets, the European stock market, and the UK stock market. The US stock market has positive correlations with all other markets for most of the sample periods, indicating the leading position of US stock market in the global stock markets. In addition, the proposed three-state VHARCJ model with Dynamic Conditional Correlation (DCC) and break structure under student-t distribution has a superior density forecast performance as compared to the competing models. The forecast models with structural breaks outperform those without structural breaks based on the log predicted likelihood, the log Bayesian factor, and the root mean square loss function.     

The effects of overnight events on daytime trading sessions

This study investigates the association between overnight and daytime-trading session returns in U.S. equity markets over the last 14 years and interprets it using the overreaction hypothesis. To identify the effects of overnight overreactions on daytime trading sessions, we control for daily investor sentiment, firms' fundamental variables, and risk factors. Our results suggest that investors tend to overreact overnight and react more dispassionately during daytime trading sessions. Investors' reactions differ across sectors, and the degree of overreaction is greater in cyclical industries than in defensive industries. Additionally, we analyze the impacts of overnight reactions on daytime trading sessions focusing on recession periods. The impacts differ by subperiods and are pronounced during the Global Financial Crisis and the onset of the COVID-19 pandemic. Investors' reactions to overnight news events also respond differently to demand and supply shock-induced recessions.     

Turbocharging Monte Carlo pricing for the rough Bergomi model

The rough Bergomi model, introduced by Bayer et al. [Quant. Finance, 2016, 16(6), 887–904], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, we focus on reducing the runtime-adjusted variance of Monte Carlo implied volatilities, thereby contributing to the model’s calibration by simulation. We employ a novel composition of variance reduction methods, immediately applicable to any conditionally log-normal stochastic volatility model. Assuming one targets implied volatility estimates with a given degree of confidence, thus calibration RMSE, the results we demonstrate equate to significant runtime reductions—roughly 20 times on average, across different correlation regimes.     

Market heterogeneities and the causal structure of volatility

Abstract

The correlation between historical and realized volatilities is studied empirically for a large range of time intervals. Similarly, the correlation between the volatility changes and the realized volatilities is studied. Both quantities measure the response functions of the market participants. These correlations show explicitly the heterogeneous structure of the market according to the characteristic time horizons of the different agents. It reveals a volatility cascade from long to short time horizons, with a structure different from the one observed in turbulence. A comparison is made with several theoretical processes used in finance, allowing a better understanding of the role and interactions of the market participants (intra-day trader, portfolio manager, central banks, pension funds, …). Moreover, we have developed a new ARCH-type process that incorporates the different groups of agents, with their characteristic memories. This process reproduces well the empirical response function, and allows us to quantify the importance of each group.     

Do negative and positive equity returns share the same volatility dynamics?

This paper investigates whether positive and negative returns share the same dynamic volatility process. The well established stylized facts on volatility persistence and asymmetric effects are re-examined in light of such dichotomy. To analyze the dynamics of down and up volatilities estimated from daily returns I use a bivariate generalization of the standard EGARCH model. As a robustness check, I also investigate various specifications of down and up realized measures estimated from high-frequency data. The empirical findings point to the existence of a marked diversity in the volatilities of positive and negative daily returns in terms of persistence and sensitivity to good and bad news. A simple forecasting exercise highlights the striking performance of the proposed approach even during the crisis period.     

Volatility linkages of the equity,bond and money markets: an implied volatility approach

This study proposes an alternative approach for examining volatility linkages between Standard & Poor's 500, Eurodollar futures and 30 year Treasury Bond futures markets using implied volatility from the three markets. Simple correlation analysis between implied volatilities in the three markets is used to assess market correlations. Spurious correlation effects are considered and controlled for. I find that correlations between implied volatilities in the equity, money and bond markets are positive, strong and robust. Furthermore, I replicate the approach of Fleming, Kirby and Ostdiek (1998) to check the substitutability of the implied volatility approach and find that the results are nearly identical; I conclude that my approach is simple, robust and preferable in practice. I also argue that the results from this paper provide supportive evidence on the information content of implied volatilities in the equity, bond and money markets.     

Options on realized variance by transform methods: a non-affine stochastic volatility model

In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model by developing efficient transform-based pricing methods. This non-affine model gives prices of options on realized variance that allow upward-sloping implied volatility of variance smiles. Heston's model [Rev. Financial Stud., 1993, 6, 327–343], the benchmark affine stochastic volatility model, leads to downward-sloping volatility of variance smiles—in disagreement with variance markets in practice. Using control variates, we propose a robust method to express the Laplace transform of the variance call function in terms of the Laplace transform of the realized variance. The proposed method works in any model where the Laplace transform of realized variance is available in closed form. Additionally, we apply a new numerical Laplace inversion algorithm that gives fast and accurate prices for options on realized variance, simultaneously at a sequence of variance strikes. The method is also used to derive hedge ratios for options on variance with respect to variance swaps.     

A spot market model for pricing derivatives in electricity markets

Abstract

In this paper, we analyse the evolution of prices in deregulated electricity markets. We present a general model that simultaneously takes into account the following features: seasonal patterns, price spikes, mean reversion, price dependent volatilities and long term non-stationarity. We estimate the parameters of the model using historical data from the European Energy Exchange. Finally, we demonstrate how it can be used for pricing derivatives via Monte Carlo simulation.     

Simultaneous volatility transmissions and spillover effects: U.S. and Hong Kong stock and futures markets

Contemporaneous transmission effects across volatilities of the Hong Kong Stock and Index futures markets and futures volume of trade are tested by employing a structural systems approach. Competing measures of volatility spillover, constructed from the overnight U.S. S&P500 index futures, are tested and found to impact on the Hong Kong asset return volatility and volume of trade patterns. The examples utilize intra-day 15-min sampled data from this medium-sized Asia Pacific equity and derivative exchange. Both the intra- and inter-day patterns in the Hong Kong market are allowed for in the estimation process.     

An index of market shocks based on multiscale analysis*

Abstract

Financial markets are places of sudden and violent price movements. Nevertheless, financial crises lack a universally recognized way of assessing their gravity. This has motivated the measure recently proposed and applied to the exchange rates market by Zumbach et al (2000a Int. J. Theor. Appl. Finance 3 347–55). This measure relies on an analogy with geophysics: the scale of market shocks (SMS) is equivalent to the Richter scale used for earthquakes. More precisely, as a market is the place where economic agents—with different investment horizons—interact, the SMS definition is a weighted aggregation of volatility measures corresponding to these different horizons. In this paper, we implement and apply a similar measure to stock markets, and adapt it to take into account some extra features of these markets.

The volatilities are first described, and then used to assess the market instability perceived by a market participant. The evolution of our index of market shocks (IMS)—after rescaling for easy interpretation—is presented using different computational methods.

The IMS is then compared with another multiscale measure, the multifractal spectrum width, and we also investigate the links between the IMS and the daily close-to-close returns and volatility. Finally, we describe the recent turbulence on the French market using the IMS as an exploratory tool, concluding that the events of September 2001 proved to be a major shock compared to the Russian and Asian crises.     

Overnight information flow and realized volatility forecasting

This study compares various approaches for incorporating the overnight information flow for forecasting realized volatility of the Australian index ASX 200 and seven very liquid Australian shares from March 2007 to January 2014. The analysis shows that considering overnight information separately rather than adding it to the daily realized volatility estimates leads consistently to better out-of-sample results despite the higher number of involved parameters. A novel, very promising approach is to combine the assets’ own overnight returns with realized volatility estimates of related assets from other markets for which intraday data is available while the Australian exchange is closed.