This paper shows that the VIX market contains information that is not already contained by the S&P 500 market on the variance of the S&P 500 returns. We estimate a flexible affine model based on a joint time series of underlying indexes and option prices on both markets. We find that including VIX option prices in the model estimation allows better identification of the parameters driving the risk-neutral conditional distributions and term structure of volatility, thereby enhancing the estimation of the variance risk premium. We gain new insights on the properties of the premium's term structure and show how they can be used to form trading signals. Finally, our premium has better predictive power than the usual model-free estimate and the higher-order moments of its term structure allow improving forecasts of S&P 500 returns.
Florian Auinger highlights the core weaknesses and sources of criticism regarding the VIX Index as an indicator for the future development of financial market volatility. Furthermore, it is proven that there is no statistically significant causal relationship between the VIX and the S&P 500. As a consequence, the forecastability is not given in both directions. Obviously, there must be at least one additional variable that has a strong influence on market volatility such as emotions which, according to financial market experts, are considered to play a more and more important role in investment decisions.
During the past two decades, the Cboe Volatility Index (VIX® Index), a key measure of investor sentiment and 30-day future volatility expectations, has generated much investor attention because of its unique and powerful features. The introduction of VIX futures in 2004, VIX options in 2006, and other volatility-related trading instruments provided traders and investors access to exchange-traded vehicles for taking long and short exposures to expected S&P 500 Index volatility for a particular time frame. Certain VIX-related tradable products may provide benefits when used as tools for tail-risk hedging, diversification, risk management, or alpha generation. Gauges of expected stock market volatility for various regions include the VIX Index (United States), AXVI Index (Australia), VHSI Index (Hong Kong), NVIX Index (India) and VSTOXX Index (Europe). All five of these volatility indexes had negative correlations with their related stock indexes price movements, and all five volatility indexes rose more than 50% in 2008. Although the five volatility indexes are not investable, investors can explore VIX-based benchmark indexes that show the performance of hypothetical investment strategies using VIX futures or options. Before investing in volatility-related products, investors should closely study the pricing, roll cost, and volatility features of the tradable products and read the applicable prospectuses and risk disclosure statements.
We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. The latter is increasing in risk aversion in a wide variety of economic settings. We tackle several measurement issues assessing a plethora of state-of-the-art volatility forecasting models. We then examine the predictive power of the VIX and its two components for stock market returns and economic activity. The variance premium predicts stock returns but the conditional stock market variance predicts economic activity, and is more contemporaneously correlated with financial instability than is the variance premium.
This article describes the primary uses of the VIX index in the financial literature, offering for the first time a joint view of its successes and failures in key financial areas. VIX is a model-free volatility index that measures the investor "fear" gauge due to its significant and negative relationship with S &P 500 return dynamics, which justifies its use as a proxy for market risk and volatility. This article focuses on the most frequent uses of VIX, namely, as (1) a financial product to hedge a portfolio against volatility risk; (2) a market risk measure used to analyze risk flows from financial markets and to relate private and public risks; and (3) a volatility measure to estimate the spot volatility dynamics, the volatility risk premium and volatility jumps. This survey offers an entre for researchers who consider VIX as a proxy for volatility and/or risk.
Planning for future movements in asset prices and understanding the variation in the return on assets are key to the successful management of investment portfolios. This thesis investigates issues related to modelling both asset return volatility and the large movements in asset prices that may be induced by the events in the general economy, as random processes, with the implications for risk compensation and the prediction thereof being a particular focus. Exploiting modern numerical Bayesian tools, a state space framework is used to conduct all inference, with the thesis making three novel contributions to the empirical finance literature. First, observable measures of physical and option-implied volatility on the S&P 500 market index are combined to conduct inference about the latent spot market volatility, with a dynamic structure specified for the variance risk premia factored into option prices. The pooling of dual sources of information, along with the use of a dynamic model for the risk premia, produces insights into the workings of the U.S. markets, plus yields accurate forecasts of several key variables, including over the recent period of stock market turmoil. Second, a new continuous time asset pricing model allowing for dynamics in, and interactions between, the occurrences of price and volatility jumps is proposed. Various hypotheses about the nature of extreme movements in both S&P 500 returns and the volatility of the index are analyzed, within a state space model in which the usual returns measure is supplemented by direct measures of physical volatility and price jumps. The empirical results emphasize the importance of modelling both types of jumps, with the link between the intensity of volatility jumps and certain key extreme events in the economy being drawn. Finally, an empirical exploration of an alternative framework for the statistical evaluation of price jumps is conducted, with the aim of comparing the resultant measures of return variance and jumps with those induced by more conventional methods. The empirical analysis sheds light on the potential impact of the method of measurement construction on inference about the asset pricing process, and ultimately any financial decisions based on such inference.
We use a novel pricing model to filter times series of diffusive volatility and jump intensity from S&P 500 index options. These two measures capture the ex-ante risk assessed by investors. We find that both components of risk vary substantially over time, are quite persistent, and correlate with each other and with the stock index. Using a simple general equilibrium model with a representative investor, we translate the filtered measures of ex-ante risk into an ex-ante risk premium. We find that the average premium that compensates the investor for the risks implicit in option prices, 10.1 percent, is about twice the premium required to compensate the same investor for the realized volatility, 5.8 percent. Moreover, the ex-ante equity premium that we uncover is highly volatile, with values between 2 and 32 percent. The component of the premium that corresponds to the jump risk varies between 0 and 12 percent.
We analyze the risk premia embedded in the S&P 500 spot index and option markets. We use a long time-series of spot prices and a large panel of option prices to jointly estimate the diffusive stock risk premium, the Price jump risk premium, the diffusive variance risk premium and the variance jump risk premium. The risk premia are statistically and economically significant and move over time. Investigating the economic drivers of the risk premia, we are able to explain up to 63% of these variations.
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.
Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods. Features Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products Can be used as a university textbook in a topic course on pricing variance derivatives
