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.
Master the new edge in options trades: the hidden volatility risk premium that exists in options for every major asset class. One of the most exciting areas of recent financial research has been the study of how the volatility implied by option prices relates to the volatility exhibited by their underlying assets. Here, I’ll explain the concept of the volatility risk premium, present evidence for its presence in options on every major asset class, and show how to estimate, predict, and trade on it....
In this thesis, we investigate the forecasting problem for option return and future volatility in financial market. The first part of this thesis is to study the option return skewness effect and the negative correlation between asset return and volatility. We propose a measure of ex-ante measure of option return skewness which accommodates the negative return-volatility relationship in asset returns. We investigate how time-to-expiration and moneyness affect the skewness and return of an option. Furthermore, we show that our proposed measure has extra benefits in forecasting option returns. In the second part, we test the information contents of implied volatility derived from stochastic volatility option pricing model and also examine the potential benefit of including the model’s implied volatility of volatility in forecasting future volatility and volatility risk premium. Our study finds that the inclusion of volatility of volatility factor has significantly reduced the downward bias of the slope coefficients. Most importantly, the ex-ante volatility of volatility has significant predictive power on the ex-post volatility premium. In the third part, we study the incremental benefit of adding skewness in predicting future realized volatility. The study finds that consistent with the empirical findings in the first part, realized volatility is negatively related to their skewness measure which provides a downward adjustment of the implied volatility forecast.
This book mainly addresses the general equilibrium asset pricing method in two aspects: option pricing and variance risk premium. First, volatility smile and smirk is the famous puzzle in option pricing. Different from no arbitrage method, this book applies the general equilibrium approach in explaining the puzzle. In the presence of jump, investors impose more weights on the jump risk than the volatility risk, and as a result, investors require more jump risk premium which generates a pronounced volatility smirk. Second, based on the general equilibrium framework, this book proposes variance risk premium and empirically tests its predictive power for international stock market returns.
In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.
An introduction to the theory and methods of empirical asset pricing, integrating classical foundations with recent developments. This book offers a comprehensive advanced introduction to asset pricing, the study of models for the prices and returns of various securities. The focus is empirical, emphasizing how the models relate to the data. The book offers a uniquely integrated treatment, combining classical foundations with more recent developments in the literature and relating some of the material to applications in investment management. It covers the theory of empirical asset pricing, the main empirical methods, and a range of applied topics. The book introduces the theory of empirical asset pricing through three main paradigms: mean variance analysis, stochastic discount factors, and beta pricing models. It describes empirical methods, beginning with the generalized method of moments (GMM) and viewing other methods as special cases of GMM; offers a comprehensive review of fund performance evaluation; and presents selected applied topics, including a substantial chapter on predictability in asset markets that covers predicting the level of returns, volatility and higher moments, and predicting cross-sectional differences in returns. Other chapters cover production-based asset pricing, long-run risk models, the Campbell-Shiller approximation, the debate on covariance versus characteristics, and the relation of volatility to the cross-section of stock returns. An extensive reference section captures the current state of the field. The book is intended for use by graduate students in finance and economics; it can also serve as a reference for professionals.
This is the first study on the risk-neutral 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 moments of call returns are increasing in the volatility of the underlying security, while the opposite is true for put returns. Call return moments have strong negative time-series correlation with put return moments. We find that the magnitudes of the risk-neutral and physical moments differ substantially, indicating significant option volatility, skewness, and kurtosis risk premia. The option volatility risk premium is significantly higher than the stock volatility risk premium.
Existing evidence indicates that (i) average returns of purchased delta-hedged options are negative, implying options are expensive, and (ii) volatility is the most important extra risk that is factored into option prices. Therefore, a natural extension is to explain the cross-section of average delta-hedged option returns in a stochastic volatility model. This paper solves this problem by introducing a measure of option overprice, which quantifies the impact on option prices of the volatility risk premium. It is an application of option-pricing in incomplete markets under stochastic volatility. An extensive numerical exercise shows the option overprice is consistent with the cross-section of average delta-hedged returns of calls, puts, and straddles reported by the literature for the Samp;P 500 index, except for expensive short-term out-of-the-money puts. In a stochastic volatility model, the volatility risk of at- and, especially, out-of-the-money calls and puts is several times larger than market volatility, which explains large negative volatility risk premiums if volatility risk is negative priced.
Volatility derivatives are today an important group of financial instruments. This book presents an overview of their major classes and their possible applications in investment strategies and portfolio optimization. Volatility is not constant so the book presents its term structure and its potential use in forecasting volatility.
