Common asset pricing factors in volatilities and returns in futures markets

Factor-based asset pricing models have been used to explain the common predictable variation in excess asset returns. This paper combines means with volatilities of returns in several futures markets to explain their common predictable variation. Using a latent variables methodology, tests do not reject a single factor model with a common time-varying factor loading. The single common factor accounts for up to 53% of the predictable variation in the volatilities and up to 14% of the predictable variation in the means. S&P500 futures volatility predicted by the factor model is highly correlated with volatility implied in S&P500 futures options. But both the factor and implied volatilities are significant in predicting future volatility. In derivatives pricing, both implied volatility from options and factors extracted from asset pricing models should be employed.     

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.     

Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options

We build a new class of discrete-time models that are relatively easy to estimate using returns and/or options. The distribution of returns is driven by two factors: dynamic volatility and dynamic jump intensity. Each factor has its own risk premium. The models significantly outperform standard models without jumps when estimated on S&P500 returns. We find very strong support for time-varying jump intensities. Compared to the risk premium on dynamic volatility, the risk premium on the dynamic jump intensity has a much larger impact on option prices. We confirm these findings using joint estimation on returns and large option samples.     

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.     

Optimal investment under multi-factor stochastic volatility

We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.     

The information content of implied volatilities and model-free volatility expectations: Evidence from options written on individual stocks

We measure the volatility information content of stock options for individual firms using option prices for 149 US firms and the S&P 100 index. We use ARCH and regression models to compare volatility forecasts defined by historical stock returns, at-the-money implied volatilities and model-free volatility expectations for every firm. For 1-day-ahead estimation, a historical ARCH model outperforms both of the volatility estimates extracted from option prices for 36% of the firms, but the option forecasts are nearly always more informative for those firms that have the more actively traded options. When the prediction horizon extends until the expiry date of the options, the option forecasts are more informative than the historical volatility for 85% of the firms. However, at-the-money implied volatilities generally outperform the model-free volatility expectations.     

S&P 500 Cash Stock Price Volatilities

S&P 500 stock return volatilities are compared to the volatilities of a matched set of stocks, after controlling for cross-sectional differences in firm attributes known to affect volatility. No significant difference in volatility is observed between 1975 and 1983—before the start of trade in index futures and index options. Since then, S&P 500 stocks have been relatively more volatile. The difference is statistically, but not economically, significant. The relative increase occurs primarily in daily returns and only to a lesser extent in longer interval returns. Other factors besides the start of derivative trade could be responsible for the small increase in volatility.     

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.     

Short‐Term Market Risks Implied by Weekly Options

We study short‐maturity (“weekly”) S&P 500 index options, which provide a direct way to analyze volatility and jump risks. Unlike longer‐dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment. Adopting a novel seminonparametric approach, we uncover variation in the negative jump tail risk, which is not spanned by market volatility and helps predict future equity returns. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events that are not always “signaled” by the level of market volatility and elude standard asset 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.     

Equilibrium Analysis of Portfolio Insurance

A martingale approach is used to characterize general equilibrium in the presence of portfolio insurance. Insurers sell to noninsurers in bad states, and general equilibrium requires that the risk premium rises to induce noninsurers to increase their holdings. We show that portfolio insurance increases price volatility, causes mean reversion in asset returns, raises the Sharpe ratio and volatility in bad states, and causes volatility to be correlated with volume. We also explain why out-of-the-money S&P 500 put options trade at a higher volatility than do in-the-money puts.     

Unconditional return disturbances: A non-parametric simulation approach

Simulation methods are extensively used in Asset Pricing and Risk Management. The most popular of these simulation approaches, the Monte Carlo, requires model selection and parameter estimation. In addition, these approaches can be extremely computer intensive. Historical simulation has been proposed as a non-parametric alternative to Monte Carlo. This approach is limited to the historical data available.In this paper, we propose an alternative historical simulation approach. Given a historical set of data, we define a set of standardized disturbances and we generate alternative price paths by perturbing the first two moments of the original path or by reshuffling the disturbances. This approach is either totally non-parametric when constant volatility is assumed; or semi-parametric in presence of GARCH(1, 1) volatility. Without a loss in accuracy, it is shown to be much more powerful in terms of computer efficiency than the Monte Carlo approach. It is also extremely simple to implement and can be an effective tool for the valuation of financial assets.We apply this approach to simulate pay off values of options on the S&P 500 stock index for the period 1982–2003. To verify that this technique works, the common back-testing approach was used. The estimated values are insignificantly different from the actual S&P 500 options payoff values for the observed period.     

Option-implied volatility factors and the cross-section of market risk premia

The main goal of this paper is to study the cross-sectional pricing of market volatility. The paper proposes that the market return, diffusion volatility, and jump volatility are fundamental factors that change the investors’ investment opportunity set. Based on estimates of diffusion and jump volatility factors using an enriched dataset including S&P 500 index returns, index options, and VIX, the paper finds negative market prices for volatility factors in the cross-section of stock returns. The findings are consistent with risk-based interpretations of value and size premia and indicate that the value effect is mainly related to the persistent diffusion volatility factor, whereas the size effect is associated with both the diffusion volatility factor and the jump volatility factor. The paper also finds that the use of market index data alone may yield counter-intuitive results.     

Mispriced index option portfolios

In model-free out-of-sample tests, we find that the optimal portfolio of a utility maximizing investor trading in the S&P500 Index, cash, and index options bought at ask and written at bid prices stochastically dominates the optimal portfolio without options and yields returns with higher mean and lower volatility in most months from 1990 to 2013. Unlike earlier claims of overpriced puts, our portfolios include mostly short calls and are particularly profitable when maturity is short and volatility is high. Similar results are obtained with the CAC and DAX indices. Neither priced factors nor a nonmonotonic stochastic discount factor explains the excess returns.     

A Non-Parametric Option Pricing Model: Theory and Empirical Evidence

In this paper, we propose an empirically-based, non-parametric option pricing model to evaluate S&P 500 index options. Given the fact that the model is derived under the real measure, an equilibrium asset pricing model, instead of no-arbitrage, must be assumed. Using the histogram of past S&P 500 index returns, we find that most of the volatility smile documented in the literature disappears.     

Delta-Hedged Gains and the Negative Market Volatility Risk Premium

We investigate whether the volatility risk premium is negativeby examining the statistical properties of delta-hedged optionportfolios (buy the option and hedge with stock). Within a stochasticvolatility framework, we demonstrate a correspondence betweenthe sign and magnitude of the volatility risk premium and themean delta-hedged portfolio returns. Using a sample of S&P500 index options, we provide empirical tests that have thefollowing general results. First, the delta-hedged strategyunderperforms zero. Second, the documented underperformanceis less for options away from the money. Third, the underperformanceis greater at times of higher volatility. Fourth, the volatilityrisk premium significantly affects delta-hedged gains, evenafter accounting for jump fears. Our evidence is supportiveof a negative market volatility risk premium.     

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.     

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.     

Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices

Implicit in the prices of traded financial assets are Arrow–Debreu prices or, with continuous states, the state-price density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and we derive its asymptotic sampling theory. This estimator provides an arbitrage-free method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, for example, negative skewness and excess kurtosis for asset returns, and volatility "smiles" for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.