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Variance Term Structure And Vix Futures Pricing
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Book Synopsis Variance Term Structure and VIX Futures Pricing by : Yingzi Zhu
Download or read book Variance Term Structure and VIX Futures Pricing written by Yingzi Zhu and published by . This book was released on 2005 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using no arbitrage principle, we derive a relationship between the drift term of risk-neutral dynamics for instantaneous variance and the term structure of forward variance curve. We show that the forward variance curve can be derived from options market. Based on the variance term structure, we derive a no arbitrage pricing model for VIX futures pricing. The model is the first no arbitrage model combining options market and VIX futures market. The model can be easily generalized to price other volatility derivatives.
Book Synopsis Volatility Components by : Zhongjin Lu
Download or read book Volatility Components written by Zhongjin Lu and published by . This book was released on 2008 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we analyze CBOE VIX futures price time series data from Mar. 2004 to Feb. 2008. We derive a new pricing framework for VIX futures that is convenient to study variance term structure dynamics. Our main contribution to existing literature is the identification of the number of factors implicit in VIX futures term structure. We find that three-factor model is ideal to characterize the variance term structure. We further construct and estimate structured two- and three-factor models to identify the components and find similar results.
Book Synopsis The Fine Structure of Variance by : Nicole Branger
Download or read book The Fine Structure of Variance written by Nicole Branger and published by . This book was released on 2016 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze pricing models for VIX derivatives which account for the theoretical link to stock options, taking Log-VIX models as a benchmark. We focus on up to three risk factors to model variance risk. To assess the performance of the models, we do not only look at the pricing errors, but also at the level and dynamics of the VIX' risk-neutral moments which vary considerably over time. We find that both model classes, consistent- and Log-VIX models, can reproduce the empirical patterns if three risk factors are included. In both approaches, a stochastic central tendency is of first order importance to capture the term structure of VIX futures prices, i.e. the first moment of the risk-neutral distribution. A stochastic vol-of-vol then helps to match the prices of VIX options, i.e. the higher order moments. Finally, variance jumps add the finishing touches to the model performance. All in all, consistency comes at notable costs in-sample, while out-of-sample performances are close. We find that the main difference between both model classes is the ability to capture the second moment of the VIX risk-neutral distribution.
Book Synopsis Pricing Models of Volatility Products and Exotic Variance Derivatives by : Yue Kuen Kwok
Download or read book Pricing Models of Volatility Products and Exotic Variance Derivatives written by Yue Kuen Kwok and published by CRC Press. This book was released on 2022-05-08 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis The Market for Volatility Trading; Vix Futures by : Menachem Brenner
Download or read book The Market for Volatility Trading; Vix Futures written by Menachem Brenner and published by . This book was released on 2008 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper analyses the new market for trading volatility; VIX futures. We first use market data to establish the relationship between VIX futures prices and the index itself. We observe that VIX futures and VIX are highly correlated; the term structure of VIX futures price is upward sloping while the term structure of VIX futures volatility is downward sloping. To establish a theoretical relationship between VIX futures and VIX, we model the instantaneous variance using a simple square root mean-reverting process. Using daily calibrated variance parameters and VIX, the model gives good predictions of VIX futures prices. These parameter estimates could be used to price VIX options.
Book Synopsis Risk Premia and the VIX Term Structure by : Travis L. Johnson
Download or read book Risk Premia and the VIX Term Structure written by Travis L. Johnson and published by . This book was released on 2018 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: The shape of the VIX term structure conveys information about the price of variance risk rather than expected changes in the VIX, a rejection of the expectations hypothesis. A single principal component, Slope, summarizes nearly all this information, predicting the excess returns of S&P 500 variance swaps, VIX futures, and S&P 500 straddles for all maturities and to the exclusion of the rest of the term structure. Slope's predictability is incremental to other proxies for the conditional variance risk premia, is economically significant, and can only partially be explained by variations in observable risk measures.
Book Synopsis Listed Volatility and Variance Derivatives by : Yves Hilpisch
Download or read book Listed Volatility and Variance Derivatives written by Yves Hilpisch and published by John Wiley & Sons. This book was released on 2016-10-25 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leverage Python for expert-level volatility and variance derivative trading Listed Volatility and Variance Derivatives is a comprehensive treatment of all aspects of these increasingly popular derivatives products, and has the distinction of being both the first to cover European volatility and variance products provided by Eurex and the first to offer Python code for implementing comprehensive quantitative analyses of these financial products. For those who want to get started right away, the book is accompanied by a dedicated Web page and a Github repository that includes all the code from the book for easy replication and use, as well as a hosted version of all the code for immediate execution. Python is fast making inroads into financial modelling and derivatives analytics, and recent developments allow Python to be as fast as pure C++ or C while consisting generally of only 10% of the code lines associated with the compiled languages. This complete guide offers rare insight into the use of Python to undertake complex quantitative analyses of listed volatility and variance derivatives. Learn how to use Python for data and financial analysis, and reproduce stylised facts on volatility and variance markets Gain an understanding of the fundamental techniques of modelling volatility and variance and the model-free replication of variance Familiarise yourself with micro structure elements of the markets for listed volatility and variance derivatives Reproduce all results and graphics with IPython/Jupyter Notebooks and Python codes that accompany the book Listed Volatility and Variance Derivatives is the complete guide to Python-based quantitative analysis of these Eurex derivatives products.
Book Synopsis Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models by : Anatoliy V. Swishchuk
Download or read book Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models written by Anatoliy V. Swishchuk and published by . This book was released on 2017 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estimate VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 historical data, evaluate the effect of adding jumps into asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.
Book Synopsis Trading VIX Derivatives by : Russell Rhoads
Download or read book Trading VIX Derivatives written by Russell Rhoads and published by John Wiley & Sons. This book was released on 2011-08-09 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to using the VIX to forecast and trade markets Known as the fear index, the VIX provides a snapshot of expectations about future stock market volatility and generally moves inversely to the overall stock market. Trading VIX Derivatives will show you how to use the Chicago Board Options Exchange's S&P 500 volatility index to gauge fear and greed in the market, use market volatility to your advantage, and hedge stock portfolios. Engaging and informative, this book skillfully explains the mechanics and strategies associated with trading VIX options, futures, exchange traded notes, and options on exchange traded notes. Many market participants look at the VIX to help understand market sentiment and predict turning points. With a slew of VIX index trading products now available, traders can use a variety of strategies to speculate outright on the direction of market volatility, but they can also utilize these products in conjunction with other instruments to create spread trades or hedge their overall risk. Reviews how to use the VIX to forecast market turning points, as well as reveals what it takes to implement trading strategies using VIX options, futures, and ETNs Accessible to active individual traders, but sufficiently sophisticated for professional traders Offers insights on how volatility-based strategies can be used to provide diversification and enhance returns Written by Russell Rhoads, a top instructor at the CBOE's Options Institute, this book reflects on the wide range of uses associated with the VIX and will interest anyone looking for profitable new forecasting and trading techniques.
Book Synopsis The Implied Convexity of VIX Futures by : Robert T. Daigler
Download or read book The Implied Convexity of VIX Futures written by Robert T. Daigler and published by . This book was released on 2019 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important component of theoretical CBOE Volatility Index (VIX) futures prices is a term correcting for the negative convexity of the square root function by subtracting from the forward-starting variance swap rate an estimate of the future volatility of VIX futures prices. In the same fashion that an index option's traditional implied volatility can be viewed as an aggregate market consensus of future realized volatility, this convexity value can be viewed as an aggregate market consensus of future volatility of volatility. This article examines the predictive properties and features of this convexity adjustment needed to value VIX futures prices by extracting it from the relationship between observed VIX futures prices and the corresponding spot option market prices used to compute the forward-starting variance swap rate. The authors find that implied convexity levels can indeed be used to forecast the future volatility of VIX futures prices, even though implied convexity consistently underestimates future realized VIX futures variance. They also show that implied convexity can at times violate strict theoretical conditions by being negative, although we are able to rule out arbitrage opportunities. Finally, they examine the properties of this implied convexity adjustment, both as a time series and with respect to various market volatility factors with which they find positive and statistically significant relations.
Book Synopsis Unifying Variance Swap Term Structures, SPX and VIX Derivatives by : Bo Zhao
Download or read book Unifying Variance Swap Term Structures, SPX and VIX Derivatives written by Bo Zhao and published by . This book was released on 2014 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a term structure function, a two-factor variance process and a return process to jointly price SPX and VIX derivatives. The distinctive feature of the variance model is that the factor coefficients are time-varying and they are bonded with the term structure of variance swaps. The model incorporates additional characteristics that jumps in the return process and in the variance process are more recognizable in short terms, the term structure of variance swaps is versatilely rich to be able to accommodate many desired features, and the leverage effect is stochastic. In the interest of analytical tractability, the two-factor variance process and the return process are structured by affine processes.
Book Synopsis Introduction to Derivative Securities, Financial Markets, and Risk Management, an (Third Edition) by : Robert A Jarrow
Download or read book Introduction to Derivative Securities, Financial Markets, and Risk Management, an (Third Edition) written by Robert A Jarrow and published by . This book was released on 2024-07-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition updates the text in two significant ways. First, it updates the presentation to reflect changes that have occurred in financial markets since the publication of the 2nd edition. One such change is with respect to the over-the-counter interest rate derivatives markets and the abolishment of LIBOR as a reference rate. Second, it updates the theory to reflect new research related to asset price bubbles and the valuation of options. Asset price bubbles are a reality in financial markets and their impact on derivative pricing is essential to understand. This is the only introductory textbook that contains these insights on asset price bubbles and options.
Book Synopsis Pricing Models of Volatility Products and Exotic Variance Derivatives by : Yue Kuen Kwok
Download or read book Pricing Models of Volatility Products and Exotic Variance Derivatives written by Yue Kuen Kwok and published by CRC Press. This book was released on 2022-05-08 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Explaining the Negative Returns to Volatility Products by :
Download or read book Explaining the Negative Returns to Volatility Products written by and published by . This book was released on 2016 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies returns to investing in volatility products with a primary focus on VIX futures and VIX Exchange Traded Products (ETPs). Substantial negative return premiums for these assets are documented. For example, the constant maturity portfolio of one-month VIX futures loses about 30\% per year from 2006 to 2013. The goal of the dissertation is to understand those big negative returns.The two chapters take two different and potentially complementary perspectives to look at the issue. The first chapter attempts a structural explanation and investigates if the negative VIX futures return premium is consistent with a notion of dynamic equilibrium. A model based on present value computation is derived and it endogenizes stock prices, the VIX index and its associated derivative contracts. The sizable negative volatility risk premium in the model is intuitively linked to the volatility feedback effect: increases in volatility endogenously lead to decreasing stock price. Both diffusive and jump shocks to cash flow volatility are priced in equilibrium and the market price of risk is a function of risk aversion and the ``deep" parameters that govern the dynamics of volatility. The model generates an upward sloping equilibrium VIX futures curve (contango) in steady state. The estimated model explains the negative returns as well as several other stylized features of the VIX futures, ETPs, and variance swap data. The second chapter explores whether price impact due to mechanical rolling activity of VIX ETPs contributes to the catastrophic loss. Empirical evidence is provided to support this hypothesis. The shape of the VIX future term structure is found to be significantly twisted by VIX ETPs'r rolling. The performance of VIX future indices that VIX ETPs track gets much worse after the launch of VIX ETPs. Greater amount of rolling relative to the total volume of VIX futures results in bigger loss. Front running strategies taking advantage of the price impact are shown to be very profitable right after the launch of VIX ETPs. The strategies deteriorate afterwards because VIX futures market gains more liquidity relative to VIX ETPs and also possibly because of arbitrageurs' more attention over time. In line with the price impact reasoning, VIX futures deliver abnormal daily returns when there is a directional change of trade flow by VIX ETPs.
Book Synopsis Trading Volatility by : Colin Bennett
Download or read book Trading Volatility written by Colin Bennett and published by . This book was released on 2014-08-17 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication aims to fill the void between books providing an introduction to derivatives, and advanced books whose target audience are members of quantitative modelling community. In order to appeal to the widest audience, this publication tries to assume the least amount of prior knowledge. The content quickly moves onto more advanced subjects in order to concentrate on more practical and advanced topics. "A master piece to learn in a nutshell all the essentials about volatility with a practical and lively approach. A must read!" Carole Bernard, Equity Derivatives Specialist at Bloomberg "This book could be seen as the 'volatility bible'!" Markus-Alexander Flesch, Head of Sales & Marketing at Eurex "I highly recommend this book both for those new to the equity derivatives business, and for more advanced readers. The balance between theory and practice is struck At-The-Money" Paul Stephens, Head of Institutional Marketing at CBOE "One of the best resources out there for the volatility community" Paul Britton, CEO and Founder of Capstone Investment Advisors "Colin has managed to convey often complex derivative and volatility concepts with an admirable simplicity, a welcome change from the all-too-dense tomes one usually finds on the subject" Edmund Shing PhD, former Proprietary Trader at BNP Paribas "In a crowded space, Colin has supplied a useful and concise guide" Gary Delany, Director Europe at the Options Industry Council
Book Synopsis The Volatility-of-Volatility Term Structure by : Nicole Branger
Download or read book The Volatility-of-Volatility Term Structure written by Nicole Branger and published by . This book was released on 2018 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the volatility-of-volatility (VVIX) term structure. We find that the slope of the VVIX, defined as VVIX' second principal component, predicts excess returns of S&P500 and VIX traddles. Its informational content is incremental to the VIX term structure and the variance risk premium. Thus, vol-of-vol risk matters even for stock index options. A model-based approximation for the VVIX shows that the main drivers of its term structure are continuous vol-of-vol and jump risk. Their contributions vary systematically with the state of the economy. When the latest major crises hit, continuous vol-of-vol took the lion's share over all maturities.
Book Synopsis A Note of Trading the Term Structure of VIX Futures by : Anusar Farooqui
Download or read book A Note of Trading the Term Structure of VIX Futures written by Anusar Farooqui and published by . This book was released on 2020 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term structure of VIX futures contains a very strong signal of dealer risk appetite. Unlike balance sheet quantities, this feature is available at very high frequencies. Here we exhibit two systematic strategies to mine the attendant risk premium from the term structure of expected volatility. We optimize our two hyper-parameters by OOS cross-validation. We compare our strategies to holding the S&P 500, selling short-term vol un-hedged, and a portfolio that sells short-term vol and hedges by going long on medium-term vol. We find that our strategies allow us to harvest a considerable portion of the risk premium associated with the balance sheet management of market-based intermediaries. Both in-sample and OOS, the risk-adjusted returns on our strategies are at least twice as high as the three benchmarks.
