Volatility Risk Premium Research Articles

Oil volatility risk and stock market volatility predictability: Evidence from G7 countries

Academic research relies extensively on stock market information to forecast oil volatility, with relatively little attention paid to the reverse evidence. Our paper fills this gap by investigating the predictive ability of oil volatility risk to forecast stock market volatility. Using oil volatility risk premium (oil VRP) as the predictor, we find that oil VRP does exhibit statistically and economically significant in-sample and out-of-sample forecasting power for G7 countries, even controlling for some popular macroeconomic variables. These findings are robust when using alternative proxies for volatilities of stock and oil. Furthermore, the strength of the predictive evidence is substantial during relatively high and low level of stock market, while is substantially higher for recessions vis-á-vis expansions. Oil VRP can also contains additional information for predicting a series of macroeconomic variables, which serves as an available explanation for its forecasting ability.

Volatility measures and Value-at-Risk

We evaluate and compare the abilities of the implied volatility and historical volatility models to provide accurate Value-at-Risk forecasts. Our empirical tests on the S&P 500, Dow Jones Industrial Average and Nasdaq 100 indices over long time series of more than 20 years of daily data indicate that an implied volatility based Value-at-Risk cannot beat, and tends to be outperformed by, a simple GJR-GARCH based Value-at-Risk. This finding is robust to the use of the likelihood ratio, the dynamic quantile test or a statistical loss function for evaluating the Value-at-Risk performance.The poor performance of the option based Value-at-Risk is due to the volatility risk premium embedded in implied volatilities. We apply both non-parametric and parametric adjustments to correct for the negative price of the volatility risk. However, although this adjustment is effective in reducing the bias, it still does not allow the implied volatility to outperform the historical volatility models.These results are in contrast to the volatility forecasting literature, which favors implied volatilities over the historical volatility model. We show that forecasting the volatility and forecasting a quantile of the return distribution are two different objectives. While the implied volatility is useful for the earlier objective function, it is not for the latter, due to the non-linear and regime changing dynamics of the volatility risk premium.

Volatility risk premia and future commodity returns

This paper extends the empirical literature on volatility risk premium (VRP) and future returns by analyzing the predictive ability of commodity currency VRP and commodity VRP. The empirical evidence throughout this paper provides support for a positive relationship of commodity currencies VRP and future commodity returns, but only for the period after the 2008 global financial crisis. This predictability survives the inclusion of control variables like equity VRP and past currency returns. Furthermore, gold VRP also has the ability to predict future commodity returns. However, this predictability is restricted to precious metals when control variables are considered.

Learning and forecasts about option returns through the volatility risk premium

We use learning in an equilibrium model to explain the puzzling predictive power of the volatility risk premium (VRP) for option returns. In the model, a representative agent follows a rational Bayesian learning process in an economy under incomplete information with the objective of pricing options. We show that learning induces dynamic differences between probability measuresP and Q, which produces predictability patterns from the VRP for option returns. The forecasting features of the VRP for option returns, obtained through our model, exhibit the same behaviour as those observed in an empirical analysis with S&P 500 index options.

On profitability of volatility trading on S&P 500 equity index options: The role of trading frictions

This article examines the profitability of volatility trading on S&P 500 equity index options in time-varying market conditions, with a particular focus on evaluating the authenticity of risk-adjusted returns. While significant profits are available on strategies that involve writing put options, our findings cast doubt on whether these profits can be genuinely attained in practice. After bid-ask spreads are included, we find that the profitability is significantly reduced. Furthermore, the implementation of the trades is generally difficult owing to margin requirements as investors have to set aside a large proportion of their wealth into margin accounts and also face a high likelihood of margin calls. Overall, the profitability of volatility trading tends to hinge on the capability of investors to capture the volatility risk premium and to wisely time its trades.

The Determinants of Country Risk Premium Volatility: Evidence from a Panel VAR Model

We use data for 24 European countries, spanning from 1994 to 2015, in order to examine how changes in macroeconomic conditions influence country risk premium volatility proxied by sovereign spreads variance. In the first part of the empirical analysis, we estimate the univariate generalized autoregressive conditional heteroskedasticity (GARCH) model in order to obtain the conditional variance of sovereign bond spreads. We show that an increase in this variance coincides with economic and financial crisis occurring either in the country or globally. In the second part of the empirical analysis, we estimate the panel vector autoregression (panel VAR) model in order to model the interplay between macroeconomic fundamentals (inflation, output gap, public debt and interest rates) and the country’s risk premium volatility. We show that overheating of the economy, along with an unexpected increase in public debt, inflation and interest rates, increase the country’s risk premium volatility. We also show that a sudden increase in the country´s risk premium volatility depresses the economy, exerts deflationary pressures on consumer prices, and is followed by a strong and permanent increase in public debt.

Risk Premium Spillovers Among Stock Markets: Evidence from Higher-Order Moments

This paper investigates the volatility, skewness and kurtosis risk premium spillovers among U.S., U.K., German and Japanese stock markets. We define risk premia as the difference between risk-neutral and realized moments. Our findings highlight that during periods of stress and after 2014, cross-market and cross-moment spillovers increase, and this is mirrored by a decrease in within spillovers. We document strong bi-directional spillovers between skewness and kurtosis risk premia and emphasize the prominent role played by the volatility risk premium. Finally, we show that several macroeconomic and financial factors increase with the intensity of risk premium spillovers.

Stress-Testing Volatility Risk Premium Harvesting Strategies Based on S&P 500 Index Options

The volatility risk premium (VRP), commonly accessed by writing equity index options, can help investors enhance portfolio returns. Some investors, however, have an aversion to options selling, especially put options, because they fear significant losses in a financial crisis. This article examines this aversion by analyzing the performance of two VRP-harvesting strategies based on writing out-of-the-money S&P 500 Index options (the dedicated VRP and the overlay VRP constructs) in market distress and comparing them with the S&P 500 Index. All series are stress-tested with five historical crisis episodes in the last three decades and three additional extreme scenarios modeled after the worst stock market crashes in the past century. The analysis reveals that the VRP strategies can achieve their objective of outperforming the market and mitigating investors’ losses during financial distress. The performance of the VRP constructs in a crisis depends on two main factors: the beta of the VRP strategy and the speed of the market crash. This article concludes that investors’ aversion to option selling may be unjustified and they may benefit significantly from the VRP at all times, especially in today’s market, when expected returns from traditional assets are subdued.

The Market Price of Volatility Risk and the Dynamics of Market and Actuarial Implied Volatilities

Option prices in the market embed a probability distribution over the option’s payoff, which can be fairly easily extracted. But in this risk-neutral distribution, the market’s true expectations about future returns are distorted by risk preferences, in particular, aversion to volatility risk. To separate the returns forecasts from risk aversion, one needs another way to estimate the market’s probability estimates, which the author calls “actuarial probabilities.” This difficult problem becomes even harder in the swaptions market, because the risk exposure for a swaption depends on two different time horizons. For example, a 2 × 5 swaption has two years (“expiry”) of optionality culminating with the option to enter into a swap with a maturity (“tail”) of five years. The volatility surface is three-dimensional, with two time variables and the strike interest rate (the “volatility cube”), and it is difficult to estimate statistically using available data on long-lived contracts. The author develops a procedure based on extracting a small number of common factors of the volatility process using principal components. Since all swaptions are exposed to these factors, with different loadings, modeling the evolution of the principal components, rather than the specific swaption volatilities, allows a more efficient use of the data. Applying this approach to about 10 years of swaption data, the article reports several interesting results, including the fact that three principal components capture a large proportion of the variation in actuarial volatilities across the volatility cube, while a couple extra PCs are needed to achieve the same level of explanatory power for market implied volatilities. One clear result is that the market price of volatility risk is time-varying, and it moves rather quickly, with rates of mean-reversion that seem much faster than for actuarial volatility, particularly for short expiry–long tail swaptions. Another interesting result is that the volatility risk premium reverses sign, being largely positive (market IV > actuarial IV) for contracts with short expiry, but becoming negative for long expiry contracts.

Inter-firm Relationships and Asset Prices

This paper proposes a novel link between the propagation of shocks within production networks and asset prices. It develops a dynamic network model in which the propagation of firm cash-flow shocks via inter-firm relationships affects the economy's equilibrium asset prices. When calibrated to match key features of customer-supplier networks in the United States, the model generates long-run risks, high and volatile risk premia, and a low and stable risk-free rate. Consistent with data from firms in manufacturing and service industries, the model predicts that central firms in the network command lower risk premiums than peripheral firms, and that firm-level return volatilities exhibit a high degree of co-movement.

Optimal Option Portfolio Strategies: Deepening the Puzzle of Index Option Mispricing

Traditional methods of asset allocation (such as mean–variance optimization) are not adequate for option portfolios because the distribution of returns is non-normal and the short sample of option returns available makes it difficult to estimate their distribution. We propose a method to optimize a portfolio of European options, held to maturity, with a myopic objective function that overcomes these limitations. In an out-of-sample exercise incorporating realistic transaction costs, the portfolio strategy delivers a Sharpe ratio of 0.82 with positive skewness. This performance is mostly obtained by exploiting mispricing between options and not by loading on jump or volatility risk premia.

Learning and Forecasts about Option Returns through the Volatility Risk Premium

We use learning in an equilibrium model to explain the puzzling predictive power of the volatility risk premium (VRP) for option returns. In the model, a representative agent follows a rational Bayesian learning process in an economy under incomplete information with the objective of pricing options. We show that learning induces dynamic differences between probability measures P and Q, which produces predictability patterns from the VRP for option returns. The forecasting features of the VRP for option returns, obtained through our model, exhibit the same behaviour as those observed in an empirical analysis with S&P 500 index options.

REGIME SWITCHING DETERMINANTS OF SOVEREIGN CDS SPREADS: EVIDENCE FROM TURKEY

In this study, it is assessed the main determinants of sovereign CDS spreads in Turkey from January 2006 to December 2015. Before delving into the nonlinear Markov regime-switching model estimation, a conventional one-state linear model is estimated answering to what extent the sovereign credit risk is affected in between global and country-specific market variables and by credit ratings announcement changes. In broad strokes, the regime-switching analysis reveals that among domestic variables, it is the foreign exchange rate that affects the sovereign credit risk more in more volatile periods and among global variables, the indicators standing for global volatility risk premiums and international liquidity primarily influence the changes in the sovereign CDS spread in turbulent regimes whereas proxies for global risk free rate are significant more in tranquil regimes.

Assessing Low-Volatility Assets in the LDI Framework

In the liability-driven investing (LDI) framework, an underfunded pension plan may use the glidepath approach—dividing assets for liability-matching and asset-growth purposes. This practice introduces a dilemma, as the projected funding ratio and funding ratio volatility may not be improved at the same time. Low-volatility assets may be suited in the LDI framework to resolve this dilemma. This article examines the behavior of several low-volatility assets, including three low/minimum volatility equity indexes and two alternative low-volatility series (the HFRI Fund Weighted Composite Index and a volatility risk premium–based construct), in a generic underfunded pension plan with typical assumptions. The study concludes that low-volatility investments may be a good choice for growth assets in the LDI framework, as the low-volatility profile can help pension plans reduce projected funding ratio volatility and may improve funding ratio projections. On the other hand, the benefits of low-volatility investments in the LDI framework depend on such assets continuing their past return–risk patterns into the future, an assumption that may not materialize. Pension managers are encouraged to consider low-volatility assets as potential components for underfunded pension plans, although the decision whether to include such assets in pensions depends heavily on future return assumptions.

Option Informed Stock Picking

A wide range of research has suggested that informed trading in options markets may effectively signal subsequent changes in equity prices. In this paper, we analyze the performance of long/short strategies based on a number of signals from options markets. In addition, we create an easily implemented long-only strategy based on a subset of the signals (volatility risk premium, option/stock volume ratio, implied volatility skew and realized volatility). In order to minimize transaction costs and liquidity issues we restrict our analysis to S&P 500 constituents, we rebalance our portfolio monthly and limit our holdings to 50 individual stocks. Our analysis of the period from 1996 through mid-2015 shows significant outperformance of a long-only equal weighted portfolio of 50 stocks (similar results were found when considering 10-stock portfolios), relative to the S&P 500 and the equal weighted S&P 500. A return attribution analysis confirms that the outperformance is provided by individual stock selection rather than sector selection.

The joint cross-sectional variation of equity returns and volatilities

Abstract This paper analyzes the determinants of the simultaneous cross-sectional variation of return and volatility risk premia. Independently of the model specification employed, the estimated risk premium associated with the default premium beta is always positive and statistically different from zero. Moreover, the risk premium of the market volatility risk premium beta is negative and statistically significant. However, both risk factors are priced economically and statistically differently in the volatility and return segments of the market. On average, common factors in both segments explain 90% of the variability of volatility risk premium portfolios, but only 65% of the variability of equity return portfolios.

An Asset Class Characterization of the U.S. Equity Index Volatility Risk Premium

The authors use a novel 32-year return series to study the risk, return, and predictability of a strategy that sells one-month S&P 500 variance swaps with fixed ex-ante tail risk. They find that unconditional short exposure in their sample is characterized primarily by two features: (1) a very high Sharpe ratio exceeding 1.2 and (2) a severe but infrequent crash risk. From a forecasting perspective, the authors find a generally lower premium following market sell-offs and crashes. However, they fail to find significant evidence linking returns to the level of either implied or realized volatility.

A multivariate stochastic unit root model with an application to derivative pricing

This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (STUR) models to a multivariate case including asymptotic theory for estimation of the model’s parameters. The extensions are useful for applications of STUR modeling and because they lead to a generalization of the Black–Scholes formula for derivative pricing. In place of the standard assumption that the price process follows a geometric Brownian motion, we derive a new form of the Black–Scholes equation that allows for a multivariate time varying coefficient element in the price equation. The corresponding formula for the value of a European-type call option is obtained and shown to extend the existing option price formula in a manner that embodies the effect of a stochastic departure from a unit root. An empirical application reveals that the new model substantially reduces the average percentage pricing error of the Black–Scholes and Heston’s (1993) stochastic volatility (with zero volatility risk premium) pricing schemes in most moneyness-maturity categories considered.

What Does the Volatility Risk Premium Say About Liquidity Provision and Demand for Hedging Tail Risk?

This article provides a data-driven analysis of the volatility risk premium, using tools from high-frequency finance and Big Data analytics. We argue that the volatility risk premium, loosely defined as the difference between realized and implied volatility, can best be understood when viewed as a systematically priced bias. We first use ultra-high-frequency transaction data on SPDRs and a novel approach for estimating integrated volatility on the frequency domain to compute realized volatility. From that we subtract the daily VIX, our measure of implied volatility, to construct a time series of the volatility risk premium. To identify the factors behind the volatility risk premium as a priced bias, we decompose it into magnitude and direction. We find compelling evidence that the magnitude of the deviation of the realized volatility from implied volatility represents supply and demand imbalances in the market for hedging tail risk. It is difficult to conclusively accept the hypothesis that the direction or sign of the volatility risk premium reflects expectations about future levels of volatility. However, evidence supports the hypothesis that the sign of the volatility risk premium is indicative of gains or losses on a delta-hedged portfolio.

A Survey of Three Derivative-Based Methods to Harvest the Volatility Premium in Equity Markets

The volatility risk premium (VRP), also known as the insurance risk premium (IRP), is an attractive source of extra returns that has low correlations with equities and fixed-income assets, and thus it can provide diversification benefits on top of traditional portfolio holdings. This article examines and compares the three most commonly used derivative-based methods to monetize the VRP: equity index option strategies, variance swaps, and CBOE Volatility Index (VIX) future constructs. The study analyzes both qualitatively and quantitatively the strengths and weaknesses of the three approaches, as well as their historical returns and risk profiles. More importantly, the potential for added diversification by all three approaches is discussed from an investor’s perspective. The study concludes that option strategies or VIX future constructs are more preferable than variance swaps for many investors.