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Our aim in this paper is to analytically compute the at-the-money second derivative of the Bachelier implied volatility curve as a function of the strike price for correlated stochastic volatility models. We also obtain an expression for the short-term limit of this second derivative in terms of the first and second Malliavin derivatives of the volatility process and the correlation parameter. Our analysis does not need the volatility to be Markovian and can be applied to the case of fractional volatility models, both with H<1/2 and H>1/2. More precisely, we start our analysis with an adequate decomposition formula of the curvature as the curvature in the uncorrelated case (where the Brownian motions describing asset price and volatility dynamics are uncorrelated) plus a term due to the correlation. Then, we compute the curvature in the uncorrelated case via Malliavin calculus. Finally, we add the corresponding correlation correction and we take limits as the time to maturity tends to zero. The presented results can be an interesting tool in financial modeling and in the computation of the corresponding Greeks. Moreover, they allow us to obtain general formulas that can be applied to a wide class of models. Finally, they provide us with a precise interpretation of the impact of the Hurst parameter H on this curvature.

This paper studies the predictive ability of corridor implied volatility (CIV) measure. It is motivated by the fact that CIV is measured with better precision and reliability than the model-free implied volatility due to the lack of liquid options in the tails of the risk-neutral distribution. By adding CIV measures to the modified GARCH specifications, the out-of-sample predictive ability of CIV is measured by the forecast accuracy of conditional volatility. It finds that the narrowest CIV measure, covering about 10% of the RND, dominate the 1-day ahead conditional volatility forecasts regardless of the choice of GARCH models in high volatile period; as market moves to non volatile periods, the optimal width broadens. For multi-day ahead forecasts narrow and mid-range CIV measures are favoured in the full sample and high volatile period for all forecast horizons, depending on which loss functions are used; whereas in non turbulent markets, certain mid-range CIV measures are favoured, for rare instances, wide CIV measures dominate the performance. Regarding the comparisons between best performed CIV measures and two benchmark measures (market volatility index and at-the-money Black–Scholes implied volatility), it shows that under the EGARCH framework, none of the benchmark measures are found to outperform best performed CIV measures, whereas under the GARCH and NAGARCH models, best performed CIV measures are outperformed by benchmark measures for certain instances.

The aim of this study is to examine the volatility smile based on the European options on Shanghai stock exchange 50 ETF. The data gives evidence of the existence of a well-known U-shaped implied volatility smile for the SSE 50 ETF options market in China. For those near-month options, the implied volatility smirk is also observed. And the implied volatility remains high for the short maturity and decreases as the maturity increases. The patterns of the implied volatility of SSE 50 ETF options indicate that in-the-money options and out-of-the-money options are more expensive relative to at-the-money options. This makes the use of at-the-money implied volatility for pricing out-of- or in-the-money options questionable. In order to investigate the implied volatility, the regression-based implied volatility functions model is considered employed to study the implied volatility in this study as this method is simple and easy to apply in practice. Several classical implied volatility functions are investigated in this paper to find whether some kind of implied volatility functions could lead to more accurate options pricing values. The potential determinants of implied volatility are the degree of moneyness and days left to expiration. The empirical work has been expressed by means of simple ordinary least squares framework. As the study shows, when valuing options, the results of using volatility functions are mixed. For far-month options, using at-the-money implied volatility performs better than other volatility functions in option valuation. For near-month options, the use of volatility functions can improve the valuation accuracy for deep in-the-money options or deep out-of-the-money options. However, no particular implied volatility function performs very well for options of all moneyness level and time to maturity.

This study illuminates the difference in the intraday return-volume relationships of spot and index futures. The quantile regression analyses show that the widening effect of the spot trading volume on the distribution of spot returns disappears within a short period of time, whereas that of the futures trading volume on the distribution of spot returns remains over the relatively long term. The short-term effect of the spot volume and the long-term effect of the futures volume are consistent for trading volume shocks. The findings suggest that the spot volume is primarily induced by the demand for hedging or differences of opinion, whereas the futures volume contains information about price movements.

This paper analyses the volatility transmission between European Global Systemically Important Banks (GSIBs) and implied stock market volatility. A Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity model is applied to determine the dynamic correlation between returns of Europe’s GSIBs and the world’s most prominent measure of market “fear”, the CBOE Volatility Index (VIX). The results identify a higher negative co-relationship between the VIX and GSIB returns during the COVID-19 period compared with the Global Financial Crisis (GFC), with one-day lagged changes in the VIX negatively Granger-causing bank returns. The asymmetric impact of changes in implied volatility is examined by quantile regressions, with the findings showing that in the lower quartile–where extreme negative bank returns are present–jumps in the VIX are highly significant. This effect is more pronounced during COVID-19 than during the GFC. Additional robustness analysis shows that these findings are consistent during the periods of the Swine Flu and Zika virus epidemics.

In this study, we examine the options market reaction to bank loan announcements for the population of US firms with traded options and loan announcements during 1996–2010. We get evidence on a significant options market reaction to bank loan announcements in terms of levels and changes in short-term implied volatility and its term structure, and observe significant decreases in short-term implied volatility, and significant increases in the slope of its term structure as a result of loan announcements. Our findings appear to be more pronounced for firms with more information asymmetry, lower credit ratings and loans with longer maturities and higher spreads. Evidence is consistent with loan announcements providing reassurance for investors in the short-term, however, over longer time horizons, the increase in the TSIV slope indicates that investors become increasingly unsure over the potential risks of loan repayment or uses of the proceeds.

This paper applies long-memory techniques (both parametric and semi-parametric) to examine whether Brexit has led to any significant changes in the degree of persistence of the FTSE (Financial Times Stock Index) 100 Implied Volatility Index (IVI) and of the British pound's implied volatilities (IVs) vis-à-vis the main currencies traded in the FOREX (foreign exchange market), namely the euro, the US dollar and the Japanese yen. We split the sample to compare the stochastic properties of the series under investigation before and after the Brexit referendum, and find an increase in the degree of persistence in all cases except for the British pound-yen IV, whose persistence has declined after Brexit. These findings highlight the importance of completing swiftly the negotiations with the European Union (EU) to achieve an appropriate Brexit deal.

This study investigates the relationship between the volatility risk premia (VRP) of stock and oil returns. Using daily data on VRP from 10 May 2007 to 16 May 2017, VAR analyses on the stock and oil VRP are conducted, and it is found that the effects of the stock VRP on the oil VRP are limited and, if any, short-lived. In contrast, the VRP of oil has significantly positive and long-lasting effects on the stock VRP after the financial crisis. These results suggest that investors’ sentiments (measured by VRP) are transmitted from the oil to the stock market over time, but not vice versa. This is unexpected because the financialization of commodities means a massive increase in investment in commodities by investors in the traditional stock and bond markets; hence, the direction of effects is thought to be from the stock to the commodity market.

This paper examines the dynamics of connectedness among the realized volatility indices of 16 clean energy stocks belonging to the SPGCE and the implied volatility indices of two important stock markets—the S&P 500 and the STOXX50—and two commodities markets—the crude oil and gold markets. The empirical results show a unidirectional connectedness from the implied volatility indices to the clean energy stocks. Our analysis further reveals similar volatility connectedness behaviors among companies in the same energy production subsector. However, there exists heterogeneous behavior between different energy production subsectors over time. Further, we identify pairwise directional connectedness clusters among related companies, indicating that there are few possibilities for portfolio diversification within the energy production subsectors. Finally, through an impulse–response analysis, we confirm that the expectation of future market volatility of the S&P 500 index and the gold price plays a leading role in volatility connectedness with clean energy stocks.