Risk-neutral Volatility Research Articles

Heterogeneous Volatility Information Content for the Realized GARCH Modeling and Forecasting Volatility

Abstract As the demand for accuracy in volatility modeling and forecasting increases, the literature tends to incorporate different volatility measures with heterogeneous information content to construct the hybrid volatility model. This study focuses on one of the popular hybrid volatility models: the Realized Generalized Autoregressive Heteroskedasticity (Realized GARCH) and embeds various volatility measures, including the CBOE VIX, VIX1D, Realized Volatility, and Daily Range to examine their heterogeneous impact on the conditional volatility estimation and forecasting. To evaluate the impact of the volatility measures, we first construct a volatility response function. This involves calculating the difference in one-step-ahead conditional volatility forecasts that incorporate information from both return and volatility measures against the forecasts based on return innovations only. Subsequently, the variance share is calculated to evaluate its role in explaining future variations in the Realized GARCH. Our results show that among these four volatility measures, VIX is the most informative volatility. Although VIX1D is overemphasized by the literature, its significance in volatility forecasting remains substantial, confirming that risk-neutral volatility measures are generally more informative than physical measures. Finally, we also find that incorporating multiple risk-neutral volatility measures does not improve forecasting performance compared to using a single measure due to overlapping information.

Why do rational investors like variance at the peak of a crisis? A learning-based explanation

Investors’ learning can drastically alter the dynamics of the variance risk premium: it no longer increases as economic conditions deteriorate but exhibits a highly nonlinear pattern, occasionally even turning negative. We demonstrate this intuition using a model where investors rationally form their belief about the hidden economic state. When the “bad” state becomes probable, investors start liking high future variance because it overwhelmingly correlates with lower marginal utility. This mechanism rationalizes the puzzling observation that risk-neutral volatility falls short of physical volatility at the peak of a severe crisis. Our results shed light on the interpretation of good economic uncertainty.

Spillover dynamics effects between risk-neutral equity and Treasury volatilities

Macro-finance asset pricing models provide a rationale for connectedness dynamics between equity and Treasury risk-neutral volatilities. In this paper, we study the total and directional connectedness, in the sense of spillover effects, between risk-neutral volatilities from the equity and Treasury markets. In addition, we analyze the economic and monetary drivers of connectedness dynamics. Most of the time, but especially during bad economic times, we find significant net spillovers from Treasury to equity risk-neutral volatility. The spillover channel between risk-neutral volatilities arises mainly through the government fixed income market.

Can risk-neutral skewness and kurtosis subsume the information content of historical jumps?

We examine the relation between jump variations and risk-neutral moments in volatility forecasting. We propose a method that involves no extrapolation in computing the risk-neutral moments of Bakshi et al. (2003) and document that risk-neutral skewness and kurtosis subsume the information content of historical jumps. While historical jumps have significant explanatory power for future volatility and such power is actually not weakened by the inclusion of risk-neutral volatility in models, their predictability does disappear when risk-neutral skewness and kurtosis are included.

Technical Note—Options Portfolio Selection

We develop a new method to optimize portfolios of options in a market where European calls and puts are available with many exercise prices for each of several potentially correlated underlying assets. We identify the combination of asset-specific option payoffs that maximizes the Sharpe ratio of the overall portfolio: such payoffs form the unique solution to a system of integral equations, which reduces to a linear matrix equation under discrete representations of the underlying probabilities. Even when risk-neutral volatilities are all higher than physical volatilities, it can be optimal to sell options on some assets while buying options on other assets, for which the positive hedging demand outweighs negative demand stemming from asset-specific returns.

The conditional expected market return

We derive lower and upper bounds on the conditional expected excess market return that are related to risk-neutral volatility, skewness, and kurtosis indexes. The bounds can be calculated in real time using a cross section of option prices. The bounds require a no-arbitrage assumption, but they do not depend on distributional assumptions about market returns or past observations. The bounds are highly volatile, positively skewed, and fat-tailed. They imply that the term structure of expected excess holding period returns is decreasing during turbulent times and increasing during normal times and that the expected excess market return is on average 5.2%.

Dissecting skewness under affine jump-diffusions

Abstract This paper derives the theoretical skewness in a five-factor affine jump-diffusion model with stochastic variance and jump intensity, and jumps in prices and variances. Numerical analysis shows that all of the uncertainties in this model affect skewness. The information regarding jumps in prices is mainly reflected in the short-term skewness. The skewness for other maturities carries the information that is highly correlated with variance. Furthermore, the theoretical VIX and skewness under a simplified five-factor model are used to fit the market risk-neutral volatility and skewness sequentially. The fitting performances are better than traditional double-jump models.

Informative Option Portfolios in Unscented Kalman Filter Design for Affine Jump Diffusion Models

Option pricing models are tools for pricing and hedging derivatives. Good models are complex and the econometrician faces many design decisions when bringing them to the data. I show that strategically constructed low-dimensional filter designs outperform those that try to use all the available option data. I construct Unscented Kalman Filters around option portfolios that aggregate option data, and track changes in risk-neutral volatility and skewness. These low-dimensional filters perform equivalently to or better than standard approaches that treat full option panels. The performance advantage is greatest in empirically relevant settings: in models with strongly skewed jump components that are not driven by Brownian volatility.

Intraday information from S&P 500 Index futures options

In this paper, we employ the intraday transaction prices of liquid E-mini S&P 500 index futures options to form 10-min ahead risk-neutral skewness forecasts and show profitable options trading strategy net of transaction costs. We do not find profitable trading based on 10-min ahead risk-neutral volatility and only very marginal cases of profitable trading using kurtosis forecasts. The skewness profitability anomaly may be an indication of informational inefficiency in intraday S&P 500 futures options trading, which is contrary to findings using longer-span daily and weekly moments. Our results lend credence to the persistence of intraday trading activities in the markets.

Is trading in the shortest-term index options profitable?

The aim of this study is to examine the return rates of the TAIEX options with at most 8 calendar days to maturity using a buy-and-hold strategy. Although our results generally reveal that the index option returns are significantly negative, we also find that whilst the return rates of monthly-expiring calls are inferior to those of weekly-expiring calls, the return rates of monthly puts tend to be less negative than those of weekly puts. Furthermore, as monthly (weekly) options approach their maturity dates, the underlying index returns are found to be negative (positive). Risk-neutral volatility and skewness are used to measure the respective fear and pessimism levels among investors towards the stock market, and indeed, we find that as the expiration date approaches, there is a discernible increase in both the fear and pessimism of investors with regard to monthly options, as compared to a reduction for weekly options.

Big moves of mutual funds

Previous research suggests that short-sellers correctly anticipate that big moves by one or more mutual funds cause temporary price distortions. By moving in the opposite direction to those trades, short-sellers outsmart mutual funds. This appears to be healthy for the overall market, but mutual funds’ vulnerability substantially reduces their profits. For informed traders, the equity lending market and the options market are substitutes for one another. In this paper, I empirically investigate how big moves of mutual funds affect the cross-section of option prices. Overall, I find strong empirical evidence for directional trading in index options. The flow-induced bearish trading activity of short-sellers is price destabilizing and greatly influences put and call option prices. Firstly, in line with the short-selling channel, inflows into mutual funds mainly impact the pricing of put options. The demand for out-of-the money put options leads to a significant drop in risk-neutral skewness. Secondly, inflows (outflows) affect the risk-neutral volatility negatively (positively); the impact on prices is consistent across put and call options. Thirdly, while the effect on risk-neutral skewness is associated with the unexpected component (based on same-day flows) only, the effect on risk-neutral volatility is associated with the unexpected and the expected component (based on prior days’ trading). Finally, while the negative relationship of inflows on risk-neutral volatility and skewness is consistent over time, the effect of outflows on risk-neutral volatility is not observable in bearish markets.

Risk-neutral moments in the crude oil market

In this paper, we provide a comprehensive study on the higher-order risk-neutral moments (RNMs) and differences in RNMs (DRNMs) in the crude oil market, implied by options written on the United States Oil Fund (USO). Based on the t-statistic, the in-sample and the out-of-sample R2 statistics, we compare the USO return predictability and USO option return predictability by using RNMs and DRNMs from May 2007 to April 2016. We find that (i) all RNMs have a poor out-of-sample performance of predicting USO returns and simple option returns, while the risk-neutral volatility (VOL) outperforms in terms of both in-sample and out-of-sample predicting delta-hedged option returns; (ii) most of the DRNMs can significantly predict the future USO returns, and (iii) differences in the risk-neutral third cumulant (DTC) and differences in the risk-neutral fourth cumulant (DFC) are two important predictors for the future USO option returns.

Option-implied objective measures of market risk

Foster and Hart (2009) introduce an objective measure of the riskiness of an asset that implies a bound on how much of one’s wealth is ‘safe’ to invest in the asset while (a.s.) guaranteeing no-bankruptcy in the long run. In this study, we translate the Foster-Hart measure from static and abstract gambles to dynamic and applied finance using nonparametric estimation of risk-neutral densities from S&P 500 call and put option prices covering 2003 to 2013. This exercise results in an option-implied market view of objective riskiness. The dynamics of the resulting ‘option-implied Foster-Hart bound’ are analyzed and assessed in light of well-known risk measures including value at risk, expected shortfall and risk-neutral volatility. The new measure is shown to be a significant predictor of ahead-return downturns. Furthermore, it is able to grasp more characteristics of the risk-neutral probability distributions than other measures, furthermore exhibiting predictive consistency. The robustness of the risk-neutral density estimation method is analyzed via a bootstrap.

The Conditional Expected Market Return

We derive lower and upper bounds on the conditional expected excess market return that are related to risk-neutral volatility, skewness, and kurtosis indexes. The bounds can be calculated in real time using a cross section of option prices. The bounds require a no-arbitrage assumption, but do not depend on distributional assumptions about market returns or past observations. The bounds are highly volatile, positively skewed, and fat tailed. They imply that the term structure of expected excess holding period returns is decreasing during turbulent times and increasing during normal times, and that the expected excess market return is on average 5.2%.

Practical Applications of What Goes into Risk-Neutral Volatility? Empirical Estimates of Risk and Subjective Risk Preferences

The Black–Scholes option-pricing model doesn’t work in the real world because option prices embed both the market’s estimate of the empirical returns distribution as well as investors’ risk attitudes. These influences are reflected in the risk-neutral probability distribution, which can be extracted from option prices without restrictive assumptions from a pricing model. In What Goes into Risk-Neutral Volatility? Empirical Estimates of Risk and Subjective Risk Preferences, published in the Fall 2016 issue of The Journal of Portfolio Management, Stephen Figlewski, professor of finance at NYU’s Stern School of Business, finds that risk-neutral volatility is strongly influenced by investors’ projections of future realized volatility and by the risk-neutralization process. Several significant variables, including the daily trading range and tail risk, are connected in different ways to realized volatility, while other variables reflect risk attitudes, such as the levels of consumer and investor confidence. This report and the original article will be of particular interest to investors and academics who seek to bridge the gap between theory and practice. TOPICS:Options, quantitative methods, tail risks

Practical Applications of What Goes into Risk-Neutral Volatility? Empirical Estimates of Risk and Subjective Risk PreferencesWhat Goes into Risk-Neutral Volatility? Empirical Estimates of Risk and Subjective Risk Preferences Stephen Figlewski

Practical Applications of What Goes into Risk-Neutral Volatility? Empirical Estimates of Risk and Subjective Risk PreferencesWhat Goes into Risk-Neutral Volatility? Empirical Estimates of Risk and Subjective Risk Preferences Stephen Figlewski

The Risk-Neutral Distribution of Option Returns

Options provide a payoff structure that is very attractive to lottery investors. Despite the growing importance of options in investors' portfolios, little is known about the actual distribution of option returns. We derive solutions for the risk-neutral variance, skewness, and kurtosis of call and put option returns and document several properties of these ex-ante moments. We find that the volatility, skewness, and kurtosis of both call and put returns are higher (lower) for options that are further out-of-the-money (in-the-money). The risk-neutral volatility of call returns is higher for options with shorter times to expiration, while the risk-neutral skewness and kurtosis are higher for calls with longer times to expiration. For put options, all three moments are higher for short-maturity options. The risk-neutral moments of call returns are increasing in the volatility of the underlying security, while the opposite is true for put returns. Risk-neutral call return moments exhibit strong positive time-series correlation, as do put return moments. Call return moments have strong negative time-series correlation with put return moments. Comparing the risk-neutral return moments to physical return moments, we find that the magnitudes of the risk-neutral and physical moments differ substantially, indicating risk premia associated with option return moments.

What Goes into Risk-Neutral Volatility? EmpiricalEstimates of Risk and Subjective Risk Preferences

Under Black–Scholes (BS) assumptions, empirical volatility and risk-neutral volatility are given by a single parameter that captures all aspects of risk. Inverting the model to extract implied volatility from an option’s market price gives the market’s forecast of future empirical volatility. But real world returns are not lognormal, volatility is stochastic, and arbitrage is limited; thus, option prices embed both the market’s estimate of the empirical returns distribution and also investors’ risk attitudes, including possibly distinct preferences over different volatility-related aspects of the returns process, such as tail risk. All these influences are reflected in the risk-neutral density (RND), which can be extracted from option prices without requiring restrictive assumptions from a pricing model. The author computes daily RNDs for the SP others reflect risk attitudes, such as the level of investor confidence and the size of recent volatility forecast errors.

Mutual Funds, Price Pressure, and Index Options

As research has begun to focus on the fact of less-than-infinite liquidity in real-world financial markets, evidence has begun to accumulate on price effects caused by large trades. Cash inflows into index-based mutual funds can be large and potentially highly correlated across “herding” investors, resulting in flow-induced price effects on the index stocks. In this article, Lehnert shows that mutual fund inflows, which have been shown to push prices of illiquid stocks too far at first only to be followed by predictable reversals later, also affect index options in the form of negative shocks to risk-neutral skewness. Among the interesting results are that inflows are more powerful than outflows; only the unexpected portion of the flow seems to matter; and the effect is largely limited to short maturity options. The article goes on to consider risk-neutral volatility and kurtosis, finding behavior largely consistent with the fund flow hypothesis.

What Goes into Risk Neutral Volatility? Empirical Estimates of Risk and Subjective Risk Preferences

Under Black-Scholes (BS) assumptions, empirical volatility and risk neutral volatility are given by a single parameter, which captures all aspects of risk. Inverting the model to extract implied volatility from an option's market price gives the market's forecast of future empirical volatility. But real world returns are not lognormal, volatility is stochastic, and arbitrage is limited, so option prices embed both the market's estimate of the empirical returns distribution and also investors' risk attitudes, including possibly distinct preferences over different volatility-related aspects of the returns process, such as tail risk. All of these influences are reflected in the risk neutral density (RND), which can be extracted from option prices without requiring restrictive assumptions from a pricing model.We compute daily RNDs for the SP others reflect risk attitudes, such as the level of investor confidence and the size of recent volatility forecast errors.