Download or read book Modelling the Variance Risk Premium of Equity Indices written by Andrea Granelli and published by . This book was released on 2014 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding variance risk is of key importance in mathematical finance since it affects risk management, asset allocation and derivative pricing. Variance risk is priced in financial markets by the so-called variance risk premium (VRP), which refers to the premium demanded for holding assets whose variance is exposed to stochastic shocks.This paper identifies a new modelling framework for equity indices and presents for the first time explicit analytical formulas for their VRP in a multivariate stochastic volatility setting, which includes multivariate non-Gaussian Ornstein-Uhlenbeck processes and Wishart processes. Moreover, we propose to incorporate contagion within the equity index via a multivariate Hawkes process and find that the resulting dynamics of the VRP represent a convincing alternative to the models studied in the literature up to date.We show that our new model can explain the key stylised facts of both equity indices and individual assets and their corresponding VRP, while popular (multivariate) stochastic volatility models fail.We finally prove the existence of a structure-preserving risk neutral measure for our model. In particular, we establish the class of equivalent probabilities that preserve the self-affecting structure of the Hawkes process.

Download or read book Variance Risk Premium Demystified written by Grigory Vilkov and published by . This book was released on 2008 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the dynamics and cross-sectional properties of the variance risk premia embedded in options on stocks and indices, approximated by the synthetic variance swap returns. Several important stylized facts and contributions arise. First, variance risk premia for indices are systematically larger (more negative) than for individual securities. Second, there are systematic cross-sectional differences in the price of variance in individual stocks. Linking variance swaps to firm size/book-to-market, and stock turnover characteristics, an investor gains access to several lucrative long-short strategies with Sharpe Ratios around 2.85. Third, principal component analysis reveals at most one important factor driving both stock and variance swap returns, which corresponds to the traditional market factor. For the remainder of the dynamics, the stock and its variance processes are nearly linearly independent. Fourth, we find the leverage effect through analysis of the relationship between the variance risk premium and stock to variance correlation. The systematic (market factor) part of the leverage effect provides additional evidence of the existence of one factor common to both variance swaps and stocks, but the contribution of the market risk premium to the total variance premium is very small. These findings stress the importance of using variance-based instruments in the portfolio of an investor.

Download or read book Term Structure of Variance Risk Premium and Returns Predictability written by Giacomo Bormetti and published by . This book was released on 2016 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive an analytic relation between equity risk premium and the term structure of variance risk premium (VRP). Motivated by this result, we estimate the VRP term structure using a general and fully analytical discrete-time option pricing framework featuring multiple volatility components and multiple risk premia. We confirm the importance of VRP in improving option pricing performances and show the ability of multi-component GARCH models to produce realistic hump-shaped VRP term structure. We finally uncover the strong predictive power of the shape of the VRP term structure, summarized by its slope, on future stock-index returns.

Download or read book The Variance Risk Premium in Equilibrium Models written by Geert Bekaert and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equity variance risk premium is the expected compensation earned for selling variance risk in equity markets. The variance risk premium is positive and shows moderate persistence. High variance risk premiums coincide with the left tail of the consumption growth distribution shifting down. These facts, together with a positive, yet moderate, difference between the risk-neutral entropy and variance of the aggregate market return, refute the bulk of the extant consumption-based asset pricing models. We introduce a tractable habit model that does fit the data. In the model, the variance risk premium depends positively (negatively) on "bad" ("good") consumption growth uncertainty.

Download or read book Volatility of Volatility Expected Stock Return and Variance Risk Premium written by Ruoyang Wang and published by . This book was released on 2015 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory suggests a relationship between both volatility of volatility, variance risk premium, and the equity risk premium. We empirically investigate the relationship between volatility of volatility and the equity risk premium, and the relationship between the variance risk premium and the equity risk premium. We find that volatility of volatility alone explains 5 to 10% of the total variation of equity risk premium, and together with VIX data, it explains more than 20% of the total variation of equity premium. We fail to find a significant relationship between volatility of volatility and the variance risk premium.We use six measures of volatility of volatility based on non-parametric models, a GARCH model and VVIX data.

Download or read book Conditional Equity Risk Premia and Realized Variance Jump Risk written by Zhanglong Wang and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study explores the relationship between realized variance jump risk and conditional equity risk premium. Using high frequency records of the Standard & Poor's 500 index, we construct a realized variance measure and estimate its jump component using a Heterogeneous Autoregressive model augmented by a jump component. We find strong evidence that the realized variance jump risk measure significantly relates to excess stock market returns in-sample and out-of-sample from 1998 to 2010. Further, the predictive power of the variance jump remains both statistically and economically significant after controlling for commonly-used return predictors, and is also independent from variance risk premium and price jump risk. Calibration-based evidence is also consistent with our empirical findings.

Download or read book Systematic Variance Risk and Firm Characteristics in the Equity Options Market written by Vadim di Pietro and published by . This book was released on 2007 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct synthetic variance swap returns from prices of traded options to investigate the pricing of systematic variance risk in the equity options market. Cross sectional tests reveal no evidence of a negative market variance risk premium. Furthermore, we show that a class of linear factor models cannot simultaneously explain index and equity option prices. In particular, equity options appear to be underpriced relative to index options. To exploit the mispricing, we analyze an investment strategy known as dispersion trading, which is implemented by going long a portfolio of equity options, and short a portfolio of index options. After transaction costs, the strategy generates a Sharpe ratio which is more than four times greater than that of the market. We also find that equity option prices are related to underlying firm characteristics: Options on small and value stocks are more expensive than options on large and growth stocks, respectively. We find that these results are not explained by di.erential exposure to risk factors, nor by market microstructure considerations. One interpretation is that investors overestimate risk on small and value stocks. This finding provides a new context for understanding the size and value anomalies in stock returns: It suggests that investors expect higher rates of return on small and value stocks because they perceive them to be riskier than they truly are.

Download or read book Credit Risk Modeling written by David Lando and published by Princeton University Press. This book was released on 2009-12-13 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Credit risk is today one of the most intensely studied topics in quantitative finance. This book provides an introduction and overview for readers who seek an up-to-date reference to the central problems of the field and to the tools currently used to analyze them. The book is aimed at researchers and students in finance, at quantitative analysts in banks and other financial institutions, and at regulators interested in the modeling aspects of credit risk. David Lando considers the two broad approaches to credit risk analysis: that based on classical option pricing models on the one hand, and on a direct modeling of the default probability of issuers on the other. He offers insights that can be drawn from each approach and demonstrates that the distinction between the two approaches is not at all clear-cut. The book strikes a fruitful balance between quickly presenting the basic ideas of the models and offering enough detail so readers can derive and implement the models themselves. The discussion of the models and their limitations and five technical appendixes help readers expand and generalize the models themselves or to understand existing generalizations. The book emphasizes models for pricing as well as statistical techniques for estimating their parameters. Applications include rating-based modeling, modeling of dependent defaults, swap- and corporate-yield curve dynamics, credit default swaps, and collateralized debt obligations.

Download or read book A Non Linear Dynamic Model of the Variance Risk Premium written by Bjorn Eraker and published by . This book was released on 2014 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a new class of non-linear diffusion processes for modeling financial markets data. Our non-linear diffusions are obtained as transformations of affine processes. We show that asset-pricing and estimation is possible and likelihood estimation is straightforward. We estimate a non-linear diffusion model for the VIX index under both the objective measure and the risk-neutral measure where the latter is obtained from futures prices. We find evidence of significant non-linearity under both measures. We define the difference between the P and Q drift as a measure of the variance risk premium and show that it has strong predictive power for stock returns.

Download or read book The Skew Risk Premium in the Equity Index Market written by Roman Kozhan and published by . This book was released on 2019 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We measure the skew risk premium in the equity index market through the skew swap. We argue that just as variance swaps can be used to explore the relationship between the implied variance in option prices and realized variance, so too can skew swaps be used to explore the relationship between the skew in implied volatility and realized skew. Like the variance swap, the skew swap corresponds to a trading strategy, necessary to assess risk premia in a model-free way. We find that almost half of the implied volatility skew can be explained by the skew risk premium. We provide evidence that skew and variance premia are manifestations of the same underlying risk factor in the sense that strategies designed to exploit one of the risk premia but to hedge out the other make zero excess returns.

Download or read book Asset Allocation Risk Management and the Variance Risk Premium written by Giacomo Allori and published by LAP Lambert Academic Publishing. This book was released on 2011-09 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation shows the practical usefulness for asset allocation and risk management purposes of the variance risk premium, an index of market implied risk aversion. With reference to the asset allocation application, the short term forecasting ability of the variance risk premium is tested in a real time experiment by simulating long/ short quarterly rebalanced portfolios invested in the S&P500 based on the prediction of econometric models incorporating the premium. The result indicates that the use of the risk aversion index allows the Investor to outperform both the buy and hold strategy as well as similar strategies not including the risk premium both on a risk adjusted basis as well an on an absolute return one. With reference to the risk management application of the risk aversion index, we modify the filtered historical simulation approach to computation of the value at risk by relaxing the assumption of random walk and replace the model drift with a time varying conditional expectation of short-term stock returns. We find that there is little evidence that value at risk models can be improved with the predictability associated with the variance risk premium.

Download or read book General Equilibrium Option Pricing Method Theoretical and Empirical Study written by Jian Chen and published by Springer. This book was released on 2018-04-10 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Equity Risk Premium written by William N. Goetzmann and published by Oxford University Press. This book was released on 2006-11-16 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the return to investing in the stock market? Can we predict future stock market returns? How have equities performed over the last two centuries? The authors in this volume are among the leading researchers in the study of these questions. This book draws upon their research on the stock market over the past two dozen years. It contains their major research articles on the equity risk premium and new contributions on measuring, forecasting, and timing stock market returns, together with new interpretive essays that explore critical issues and new research on the topic of stock market investing. This book is aimed at all readers interested in understanding the empirical basis for the equity risk premium. Through the analysis and interpretation of two scholars whose research contributions have been key factors in the modern debate over stock market perfomance, this volume engages the reader in many of the key issues of importance to investors. How large is the premium? Is history a reliable guide to predict future equity returns? Does the equity and cash flows of the market? Are global equity markets different from those in the United States? Do emerging markets offer higher or lower equity risk premia? The authors use the historical performance of the world's stock markets to address these issues.

Download or read book Real Time Learning Macroeconomic Uncertainty and the Variance Risk Premium written by Daniele Bianchi and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The variance risk premium represents the compensation paid to index option sellers for the risk of losses following upward movements in realized market return volatility. Common wisdom connects these spikes with elevated uncertainty on economic fundamentals. I incorporate this link within a single-agent general equilibrium model, embedding real-time learning on state variables and parameters. I show that infrequent, large and relatively transitory macroeconomic uncertainty shocks produce a sizable and volatile variance risk premium. These shocks coincide with major events such as the LTCM/Russian crisis, the onset of the second Gulf War, and the great financial crisis of 2008-2009. I compute macroeconomic uncertainty as the dispersion of the agent's belief about the expected growth rate of consumption. Its time-varying nature reflects in the variance risk premium, generating short-term predictability for market excess returns, consistent with the data. In addition, the model matches the higher order moments of the realized equity premium, with a reasonably low level of relative risk aversion equal to five. I finally provide evidence that parameter uncertainty may represent an extra-source of risk which is priced in equilibrium. In fact, a model with parameter learning and standard CRRA preferences, matches around half of the historical variance risk premium.

Download or read book Variance and Skew Risk Premiums for the Volatility Market written by José Da Fonseca and published by . This book was released on 2017 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extract variance and skew risk premiums from volatility derivatives in a model-free way and analyze their relationships along with volatility index and equity index returns. These risk premiums can be synthesized through option trading strategies. Using a time series of option prices on the VIX, the most liquid volatility derivative market, we find that variance swap excess return can be partially explained by volatility index and equity index excess returns while these latter variables carry little information for the skew swap excess return. The results sharply contrast with those obtained for the equity index option market underlining very specific characteristics of the volatility derivative market.

Download or read book Small Caps in International Equity Portfolios written by Giovanna Nicodano and published by . This book was released on 2008 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: We show that predictable covariances between means and variances of stock returns may have a first order effect on portfolio composition. In an international asset menu that includes both European and North American small capitalization equity indices, we find that a three-state, heteroskedastic regime switching VAR model is required to provide a good fit to weekly return data and to accurately predict the dynamics in the joint density of returns. As a result of the non-linear dynamic features revealed by the data, small cap portfolios become riskier in bear markets, i.e. display negative co-skewness with other stock indices. Because of this property, a power utility investor ought to hold a well diversified portfolio, despite the high risk premium and Sharpe ratios offered by small capitalization stocks. On the contrary small caps command large optimal weights when the investor ignores variance risk, by incorrectly assuming joint normality of returns. These results provide the missing partial equilibrium rationale for the presence of co skewness in the empirical asset pricing models that have been proposed to explain the cross-section of stock returns.

Download or read book Essays in Volatility Modeling and Option Pricing written by Mathieu Fournier and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: