Analysing financial contagion and asymmetric market dependence with volatility indices via copulas

This paper explores the cross-market dependence between five popular equity indices (S&P 500, NASDAQ 100, DAX 30, FTSE 100, and Nikkei 225), and their corresponding volatility indices (VIX, VXN, VDAX, VFTSE, and VXJ). In particular, we propose a dynamic mixed copula approach which is able to capture the time-varying tail dependence coefficient (TDC). The findings indicate the existence of financial contagion and significant asymmetric TDCs for major international equity markets. In some situations, although contagion cannot be clearly detected by stock index movements, it can be captured by dependence between volatility indices. The results imply that contagion is not only reflected in the first moment of index returns, but also the second moment, i.e. the volatility. Results also show that dependence between volatility indices is more easily influenced by financial shocks and reflects the instantaneous information faster than the stock market indices.     

Asymmetric implied market volatility and terrorist attacks

This paper studies the impact of terrorism on implied volatility in the U.S. financial market via an event study methodology. We decompose the options-based and forward looking VIX index into its negative (VIX⁻) and positive (VIX⁺) components, extracted only from put options and call options, respectively. This decomposition of the VIX index allows us to better investigate the asymmetric impact of terrorist attacks on implied volatility from the puts and calls channels separately. Our study finds evidence of a greater impact of terror detected for the puts channel of VIX, namely VIX⁻. We further show that events that occur within the U.S. appear to impact both VIX and VIX⁻ in a similar way, whereas international terrorist attacks show a greater impact on the puts component, VIX⁻. The calls component, VIX⁺, is found to be mainly detached from terrorist attacks.     

Global financial crisis and emerging stock market contagion: A volatility impulse response function approach

By employing the volatility impulse response (VIRF) approach, this paper presents a general framework for addressing the extent of contagion effects between the BRICSs’ and U.S. stock markets and how the BRICSs’ stock markets have been influenced in the context of the 2007–2009 global financial crisis. Our empirical results show during the period of 2007–2009 global financial crisis, there are significant contagion effects from the U.S. to the BRICSs’ stock markets. Yet, the degree of stock market reactions to such shocks differs from one market to another, depending on the level of integration with the international economy. Besides, the strengthened degree of stock market integration among the U.S. and BRICS has adverse effect such that if the 2007–2009 global financial crisis occurs today it may result in heavier impact on stock market volatility nowadays compared to the crisis-era.     

Conic quantization: stochastic volatility and market implied liquidity

Market implied liquidity links the pricing of European options under stochastic volatility with the Conic Finance theory of two prices     

Global equity market leadership positions through implied volatility measures

Using unique minute-by-minute data on six major country implied volatility series, we examine the spillovers and the leadership positions of the global stock exchanges through measuring and assigning the contributions of innovations among their implied volatilities. The entire analyses are performed on synchronized transactions. A hybrid leadership methodology that is computationally efficient is employed. In nearly all cases, the findings indicate a clear relative leadership position for one or more exchanges. These, in turn, provide important insights into the operations of the markets and convey the dynamic process among them. We also address the transmission mechanism and volatility efficiency.     

Using implied volatility jumps for realized volatility forecasting: Evidence from the Chinese market

This study examines the Chinese implied volatility index (iVIX) to determine whether jump information from the index is useful for volatility forecasting of the Shanghai Stock Exchange 50ETF. Specifically, we consider the jump sizes and intensities of the 50ETF and iVIX as well as cojumps. The findings show that both the jump size and intensity of the 50ETF can improve the forecasting accuracy of the 50ETF volatility. Moreover, we find that the jump size and intensity of the iVIX provide no significant predictive ability in any forecasting horizon. The cojump intensity of the 50ETF and iVIX is a powerful predictor for volatility forecasting of the 50ETF in all forecasting horizons, and the cojump size is helpful for forecasting in short forecasting horizon. In addition, for a one-day forecasting horizon, the iVIX jump size in the cojump is more predictive of future volatility than that of the 50ETF when simultaneous jumps occur. Our empirical results are robust and consistent. This work provides new insights into predicting asset volatility with greater accuracy.     

Stock market cycles, financial liberalization and volatility

In this paper we analyze the cycles of the stock markets in four Latin American and two Asian countries, and we compare their characteristics. We divide our sample in two subperiods in order to account for differences induced by the financial liberalization processes of the early 1990s. We find that cycles in emerging countries tend to have shorter duration and larger amplitude and volatility than in developed countries. However, after financial liberalization Latin American stock markets have behaved more similarly to stock markets in developed countries whereas Asian countries have become more dissimilar. Concordance of cycles across markets has increased significantly over time, especially for Latin American countries after liberalization.     

The implied volatility smirk

This paper provides an industry standard on how to quantify the shape of the implied volatility smirk in the equity index options market. Our local expansion method uses a second-order polynomial to describe the implied volatility–moneyness function and relates the coefficients of the polynomial to the properties of the implied risk-neutral distribution of the equity index return. We present a formal, two-way representation of the link between the level, slope and curvature of the implied volatility smirk and the risk-neutral standard deviation, skewness and excess kurtosis. We then propose a new semi-analytical method to calibrate option-pricing models based on the quantified implied volatility smirk, and investigate the applicability of two option-pricing models.     

Historic risk and implied volatility

This study extends the volatility prediction literature with (1) new intraday realized volatility measures and (2) various implied volatility indexes for commodities, currencies, and equities. Predicting volatility is important for academics, investors, and regulators. Applications range from forecasting stock and option returns to constructing early warning systems. Using twenty-three Chicago Board Options Exchange VIX indexes, as opposed to the common S&P 100 and S&P 500 equity indexes, we find a bidirectional lead-lag relationship between implied volatility and realized volatility. The lead-lag relationships are more robust and stronger using suggested intraday volatility measures than using the interday volatility measures that are common in the literature.     

The 2008 financial crisis: Stock market contagion and its determinants

In this paper, we investigate worldwide contagion and its determinants during the 2008 financial crisis. Utilizing an international sample of returns from 2003 to 2009, we consider both uni- and bi-directional contagion. After controlling for crisis-related volatility, we find strong evidence that cross-market linkages increase among many financial markets. In contrast to previous crises, contagion following the 2008 global financial crisis is not confined to emerging markets. The United States and other mature financial markets in the sample transmit and receive contagion. Country markets are less influenced by regions than they are by other country markets. We also construct variables that represent relative changes in economic variables before and during the crisis. We find that both economic fundamentals such as trade structure, interest rates, inflation rates, industrial production, and regional effects, and investors’ risk aversion contribute to international contagion.     

Asymmetric information about volatility: How does it affect implied volatility,option prices and market liquidity?

This paper develops a model of asymmetric information in which an investor has information regarding the future volatility of the price process of an asset and trades an option on the asset. The model relates the level and curvature of the smile in implied volatilities as well as mispricing by the Black-Scholes model to net options order flows (to the market maker). It is found that an increase in net options order flows (to the market maker) increases the level of implied volatilities and results in greater mispricing by the Black-Scholes model, besides impacting the curvature of the smile. The liquidity of the option market is found to be decreasing in the amount of uncertainty about future volatility that is consistent with existing evidence. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stock market contagion in Central and Eastern Europe: unexpected volatility and extreme co-exceedance

We examine whether there is contagion from the US stock market to six Central and Eastern European stock markets. We use a novel measure of contagion that examines whether volatility shocks in the US stock market coupled with negative returns are followed by higher co-exceedance between US and emerging stock markets. Using our approach and controlling for a set of market-related variables, we show that during the period from 1998 to 2014, financial contagion occurred, that is, unexpected negative events in the US market are followed by higher co-exceedance between US and Central and Eastern European stock markets. Even though contagion is stronger during the financial crisis, it also occurs in tranquil times.     

Maturity cycles in implied volatility

The skew effect in market implied volatility can be reproduced by option pricing theory based on stochastic volatility models for the price of the underlying asset. Here we study the performance of the calibration of the S&P 500 implied volatility surface using the asymptotic pricing theory under fast mean-reverting stochastic volatility described in [8]. The time-variation of the fitted skew-slope parameter shows a periodic behaviour that depends on the option maturity dates in the future, which are known in advance. By extending the mathematical analysis to incorporate model parameters which are time-varying, we show this behaviour can be explained in a manner consistent with a large model class for the underlying price dynamics with time-periodic volatility coefficients.Received: December 2003, Mathematics Subject Classification (2000): 91B70, 60F05, 60H30JEL Classification: C13, G13Jean-Pierre Fouque: Work partially supported by NSF grant DMS-0071744.Ronnie Sircar: Work supported by NSF grant DMS-0090067. We are grateful to Peter Thurston for research assistance.We thank a referee for his/her comments which improved the paper.     

Dynamics of foreign exchange implied volatility and implied correlation surfaces

The prices of currency options expressed in terms of their implied volatilities and the implied correlations between foreign exchange rates at a given point in time depend on option delta and time to maturity. Implied volatilities and implied correlations likewise may thus be represented as a surface. It is well known that these surfaces exhibit both skew/smile features and term structure effects and their shapes fluctuate substantially over time. Using implied volatilities on three currency pairs as well as historical implied correlation values between them, we study the nature of these fluctuations by applying a Karhunen-Loève decomposition that is a generalization of a principal component analysis. We demonstrate that the largest share in the dynamics of these surfaces' fluctuations may be explained by exactly the same three factors, providing evidence of strong interdependences between implied correlation and implied volatility of global currency pairs.     

News implied volatility and disaster concerns

We construct a text-based measure of uncertainty starting in 1890 using front-page articles of the Wall Street Journal. News implied volatility (NVIX) peaks during stock market crashes, times of policy-related uncertainty, world wars, and financial crises. In US postwar data, periods when NVIX is high are followed by periods of above average stock returns, even after controlling for contemporaneous and forward-looking measures of stock market volatility. News coverage related to wars and government policy explains most of the time variation in risk premia our measure identifies. Over the longer 1890–2009 sample that includes the Great Depression and two world wars, high NVIX predicts high future returns in normal times and rises just before transitions into economic disasters. The evidence is consistent with recent theories emphasizing time variation in rare disaster risk as a source of aggregate asset prices fluctuations.     

The frequency of regime switching in financial market volatility

The mechanism of risk responses to market shocks is considered as stagnant in recent financial literature, whether during normal or stress periods. Since the returns are heteroskedastic, a little consideration was given to volatility structural breaks and diverse states. In this study, we conduct extensive simulations to prove that the switching regime GARCH model, under the highly flexible skewed generalized t (SGT) distribution, is remarkably efficient in detecting different volatility states. Next, we examine the switching regime in the S&P 500 volatility for weekly, daily, 10-minute and 1-minute returns. Results show that the volatility switches regimes frequently, and differences between the distributions of the high and low volatility states become more accentuated as the frequency increases. Moreover, the SGT is highly preferable to the usually employed skewed t distribution.     

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be a diffusion or a Markov process, as the examples in Sect. 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus. E. Alòs’ research is supported by grants MEC FEDER MTM 2006 06427 and SEJ2006-13537. J.A. León’s research is partially supported by the CONACyT grant 45684-F. J. Vives’ research is supported by grant MEC FEDER MTM 2006 06427.     

On the seasonality in the implied volatility of electricity options

Seasonality is an important topic in electricity markets, as both supply and demand are dependent on the time of the year. Clearly, the level of prices shows a seasonal behaviour, but not only this. Also, the price fluctuations are typically seasonal. In this paper, we study empirically the implied volatility of options on electricity futures, investigate whether seasonality is present and we aim at quantifying its structure. Although typically futures prices can be well described through multi-factor models including exponentially decreasing components, we do not find evidence of exponential behaviour in our data set. Generally, a simple linear shape reflects the squared volatilities very well as a curve depending on the time to maturity. Moreover, we find that the level of volatility exhibits clear seasonal patterns that depend on the delivery month of the futures. Furthermore, in an out-of-sample analysis we compare the performance of several implementations of seasonality in the one-factor framework.     

Implicit expectiles and measures of implied volatility

It is well known that the normal distribution is inadequate in capturing the skewed and heavy-tailed behaviour of exchange rate returns. To this end, various flexible distributions that are capable of modelling the asymmetric and tailed behaviour of returns have been proposed. In this paper, we investigate the performance of the generalized lambda distribution (GLD) to capture the skewed and leptokurtic behaviour of exchange rate returns. We do this by conducting a comprehensive numerical study to compare the performance of the GLD against the performances of the skewed t distribution, the unbounded Johnson family of distributions and the normal inverse Gaussian (NIG) distribution. Our results suggest that in terms of the value-at-risk and expected shortfall, the GLD shows at least similar performance to the skewed t distribution and the NIG distribution. Considering the ease in GLD’s use for random variate generation in Monte Carlo simulations, we conclude that the GLD can be a good alternative in various financial applications where modelling of the heavy tail behaviour is critical.