Stock price synchronicity and liquidity

We argue and provide evidence that stock price synchronicity affects stock liquidity. Under the relative synchronicity hypothesis, higher return co-movement (i.e., higher systematic volatility relative to total volatility) improves liquidity. Under the absolute synchronicity hypothesis, stocks with higher systematic volatility or beta are more liquid. Our results support both hypotheses. We find all three illiquidity measures (effective proportional bid-ask spread, price impact measure, and Amihud's illiquidity measure) are negatively related to stock return co-movement and systematic volatility. Our analysis also shows that larger industry-wide component in returns improves liquidity. We find that improvement in liquidity following additions to the S&P 500 Index is related to the stock's increase in return co-movement.     

Does social network sentiment influence the relationship between the S&P 500 and gold returns?

This study explored the relationship between investor sentiment (extracted from the StockTwits social network), the S&P 500 Index and gold returns. We investigated bilateral causality between gold prices and S&P 500 prices, the power of investor sentiment and gold returns to predict S&P 500 returns, and the influence of gold returns on S&P 500 volatility. We also considered whether the influence of sentiment varies according to the user's degree of experience. We considered the sentiment of messages that mentioned the S&P 500 Index and that users posted between 2012 and 2016. Granger causality analysis, ARIMA models and GARCH models were used for predicting S&P 500 Index returns and S&P 500 volatility. We observed a causal relationship between gold price and the S&P 500 Index. Our results also suggest that sentiment and gold returns predict S&P 500 Index returns. Finally, we observed that gold returns influence S&P 500 volatility and that the sentiment of experienced users affects S&P 500 returns.     

How Integrated are Credit and Equity Markets? Evidence from Index Options

We study the extent to which credit index (CDX) options are priced consistent with S&P 500 (SPX) equity index options. We derive analytical expressions for CDX and SPX options within a structural credit-risk model with stochastic volatility and jumps using new results for pricing compound options via multivariate affine transform analysis. The model captures many aspects of the joint dynamics of CDX and SPX options. However, it cannot reconcile the relative levels of option prices, suggesting that credit and equity markets are not fully integrated. A strategy of selling CDX volatility yields significantly higher excess returns than selling SPX volatility.     

Can we forecast the implied volatility surface dynamics of equity options? Predictability and economic value tests

We examine whether the dynamics of the implied volatility surface of individual equity options contains exploitable predictability patterns. Predictability in implied volatilities is expected due to the learning behavior of agents in option markets. In particular, we explore the possibility that the dynamics of the implied volatility surface of individual stocks may be associated with movements in the volatility surface of S&P 500 index options. We present evidence of strong predictable features in the cross-section of equity options and of dynamic linkages between the volatility surfaces of equity and S&P 500 index options. Moreover, time-variation in stock option volatility surfaces is best predicted by incorporating information from the dynamics in the surface of S&P 500 options. We analyze the economic value of such dynamic patterns using strategies that trade straddle and delta-hedged portfolios, and find that before transaction costs such strategies produce abnormal risk-adjusted returns.     

Optimal delta hedging for options

As has been pointed out by a number of researchers, the normally calculated delta does not minimize the variance of changes in the value of a trader's position. This is because there is a non-zero correlation between movements in the price of the underlying asset and movements in the asset's volatility. The minimum variance delta takes account of both price changes and the expected change in volatility conditional on a price change. This paper determines empirically a model for the minimum variance delta. We test the model using data on options on the S&P 500 and show that it is an improvement over stochastic volatility models, even when the latter are calibrated afresh each day for each option maturity. We also present results for options on the S&P 100, the Dow Jones, individual stocks, and commodity and interest-rate ETFs.     

Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets

We estimate a flexible affine model using an unbalanced panel containing S&P 500 and VIX index returns and option prices and analyze the contribution of VIX options to the model’s in- and out-of-sample performance. We find that they contain valuable information on the risk-neutral conditional distributions of volatility at different time horizons, which is not spanned by the S&P 500 market. This information allows enhanced estimation of the variance risk premium. We gain new insights on the term structure of the variance risk premium, present a trading strategy exploiting these insights, and show how to improve S&P 500 return forecasts.     

Volatility surfaces: theory,rules of thumb,and empirical evidence

Implied volatilities are frequently used to quote the prices of options. The implied volatility of a European option on a particular asset as a function of strike price and time to maturity is known as the asset's volatility surface. Traders monitor movements in volatility surfaces closely. In this paper we develop a no-arbitrage condition for the evolution of a volatility surface. We examine a number of rules of thumb used by traders to manage the volatility surface and test whether they are consistent with the no-arbitrage condition and with data on the trading of options on the S&P 500 taken from the over-the-counter market. Finally we estimate the factors driving the volatility surface in a way that is consistent with the no-arbitrage condition.     

Empirical pricing kernels

This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a time-varying pricing kernel, which we call the empirical pricing kernel (EPK). We estimate the EPK on a monthly basis from 1991 to 1995, using S&P 500 index option data and a stochastic volatility model for the S&P 500 return process. We find that the EPK exhibits counter cyclical risk aversion over S&P 500 return states. We also find that hedging performance is significantly improved when we use hedge ratios based the EPK rather than a time-invariant pricing kernel.     

Fitting prices with a complete model

The aim of this paper is to introduce some methodologies for parameter estimation in Hobson and Rogers stochastic volatility model (1998). We pay a specific attention to the so-called feedback parameter, which is shown to be crucial for the model to fit correctly the smile curve of implied volatility and we introduce different procedures for the estimation of the volatility parameters. We finally test the pricing capability of the model on market options prices on the FTSE100 and the S&P500 Indexes, according to the estimation methodologies introduced.     

Economic fundamentals or investor perceptions? The role of uncertainty in predicting long-term cryptocurrency volatility

This paper investigates the impacts of News-based Implied Volatility (NVIX) on the long-term volatility of five cryptocurrencies using the GARCH-MIDAS model. We also evaluate the hedging effectiveness of cryptocurrencies against the S&P 500 index after incorporating NVIX. The empirical results show that NVIX has a negative and significant impact on the long-term volatility of five cryptocurrencies. The impact of NVIX remains robust even after controlling for Global Economic Policy Uncertainty (GEPU) and Realized Volatility (RV). The uncertainty derived from investor perception is more important than the uncertainty of economic fundamentals in predicting cryptocurrency volatility. The hedging effectiveness of Bitcoin against the S&P 500 index is improved due to consideration of NVIX. This paper provides new evidence concerning the impacts of uncertainty on the volatility of cryptocurrencies.     

Differently motivated exchange traded fund trading activities and the volatility of the underlying index

This paper examines the correlations between two types of a market index's volatility and three trading motives of the index's exchange traded funds (ETFs). We find that ETF trading driven by belief dispersion is highly correlated with both the variance in efficient price innovations (VEPI) and the index's total volatility. Privately informed ETF trading is closely connected to the VEPI but not the total volatility, while liquidity ETF trading explains the total volatility but has little power in explaining the VEPI. Moreover, the leading ETF dominates smaller ETFs in explaining both types of volatility and often has more explanatory power than control variables.     

The Informational Role of Option Trading Volume in Equity Index Options Markets

This paper examines the dynamic relations between future price volatility of the S&P 500 index and trading volume of S&P 500 options to explore the informational role of option volume in predicting the price volatility. The future volatility of the index is approximated alternatively by implied volatility and by EGARCH volatility. Using a simultaneous equation model to capture the volume-volatility relations, the paper finds that strong contemporaneous feedbacks exist between the future price volatility and the trading volume of call and put options. Previous option volumes have a strong predictive ability with respect to the future price volatility. Similarly, lagged changes in volatility have a significant predictive power for option volume. Although the volume-volatility relations for individual volatility and volume terms are somewhat different under the two volatility measures, the results on the predictive ability of volume (volatility) for volatility (volume) are broadly similar between the implied and EGARCH volatilities. These findings support the hypothesis that both the information- and hedge-related trading explain most of the trading volume of equity index options.     

An approximate distribution of delta-hedging errors in a jump-diffusion model with discrete trading and transaction costs

We introduce a jump-diffusion model for asset returns with jumps drawn from a mixture of normal distributions and show that this model adequately fits the historical data of the S&P500 index. We consider a delta-hedging strategy (DHS) for vanilla options under the diffusion model (DM) and the proposed jump-diffusion model (JDM), assuming discrete trading intervals and transaction costs, and derive an approximation for the probability density function (PDF) of the profit-and-loss (P&L) of the DHS under both models. We find that, under the log-normal model of Black–Scholes–Merton, the actual PDF of the P&L can be well approximated by the chi-squared distribution with specific parameters. We derive an approximation for the P&L volatility in the DM and JDM. We show that, under both DM and JDM, the expected loss due to transaction costs is inversely proportional to the square root of the hedging frequency. We apply mean–variance analysis to find the optimal hedging frequency given the hedger's risk tolerance. Since under the JDM it is impossible to reduce the P&L volatility by increasing the hedging frequency, we consider an alternative hedging strategy, following which the P&L volatility can be reduced by increasing the hedging frequency.     

Volatilities implied by price changes in the S&P 500 options and futures contracts

We develop a new volatility measure: the volatility implied by price changes in option contracts and their underlying. We refer to this as price-change implied volatility. We compare moneyness and maturity effects of price-change and implied volatilities, and their performance in delta hedging. We find that delta hedges based on a price-change implied volatility surface outperform hedges based on the traditional implied volatility surface when applied to S&P 500 future options.     

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.     

Pinning in the S&P 500 futures

We show that Standard & Poor's (S&P) 500 futures are pulled toward the at-the-money strike price on days when serial options on the S&P 500 futures expire (pinning) and are pushed away from the cost-of-carry adjusted at-the-money strike price right before the expiration of options on the S&P 500 index (anti-cross-pinning). These effects are driven by the interplay of market makers' rebalancing of delta hedges due to the time decay of those hedges as well as in response to reselling (and early exercise) of in-the-money options by individual investors. The associated shift in notional futures value is at least $115 million per expiration day.     

Modeling the leverage effect with copulas and realized volatility

In this paper, we propose the use of static and dynamic copulas to study the leverage effect in the S&P 500 index. Copula models can conveniently separate the leverage effect from the marginal distributions of the return and its volatility. Daily volatility is proxied by a measure of realized volatility, which is constructed from high-frequency data. We uncover a significant leverage effect in the S&P 500 index, and this leverage effect is found to be changing over time in a highly persistent manner. Moreover the dynamic copula models are shown to outperform the static counterparts.     

Sovereign rating actions and the implied volatility of stock index options

This paper examines the interaction between the equity index option market and sovereign credit ratings. S&P and Moody's signals exhibit strong impact on option-implied volatility while Fitch's influence is less significant. Moody's downgrades reduce the market uncertainty over the rated countries' equity markets. Strong causal relationships are found between movements in the option-implied volatility and all credit signals released by S&P and Fitch, but only actual rating changes by Moody's, implying differences in rating agencies' policies. The presence of additional ratings tends to reduce market uncertainty. The findings highlight the importance of rating information in the price discovery process and offer policy implications.     

Stock and bond market interactions with level and asymmetry dynamics: An out-of-sample application

We model the dynamic interaction between stock and bond returns using a multivariate model with level effects and asymmetries in conditional volatility. We examine the out-of-sample performance using daily returns on the S&P 500 index and 10 year Treasury bond. We find evidence for significant (cross-) asymmetries in the conditional volatility and level effects in bond returns. The out-of-sample covariance matrix forecasts of the model imply that an investor is willing to pay between 129 and 820 basis points per year for using a dynamic trading strategy instead of a passive strategy.     

Periodic Stochastic Volatility and Fat Tails

This article provides a comprehensive analysis of the size andstatistical significance of the day of the week, month of theyear, and holiday effects in daily stock index returns and volatility.We employ data from the Dow Jones Industrial Average (DJIA),the S&P 500, the S&P MidCap 400, and the S&P SmallCap600 in order to test whether the seasonal patterns of mediumand small firms are similar to those of large firms. Using formalhypothesis tests based on bootstrapping, we demonstrate thatthere are more significant calendar effects in volatility thanin expected returns, especially for the two large cap indices.More importantly, we introduce the periodic stochastic volatility(PSV) model for characterizing the observed seasonal patternsof daily financial market volatility. We analyze the interactionbetween seasonal heteroskedasticity and fat tails by comparingthe performance of Gaussian PSV and fat-tailed PSVt specificationsto the plain vanilla SV and SVt benchmarks. Consistent withour model-free results, we find strong evidence of seasonalperiodicity in volatility, which essentially eliminates theneed for a fat-tailed conditional distribution, and is robustto the exclusion of the crash of 1987 outliers.