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Author : 林明賢
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (875 download)
Download or read book VIX Option Pricing Under Volatility Affine Models written by 林明賢 and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nicole Branger
Publisher :
ISBN 13 :
Total Pages : 41 pages
Book Rating : 4.:/5 (13 download)
Download or read book The Variance Process Implied in VIX Options written by Nicole Branger and published by . This book was released on 2017 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: We use the informational content of VIX derivatives to infer implications on the non-affine modeling of the stock returns' variance dynamics. We find that both a non-affine diffusion and variance jumps are necessary to capture the short- and long-term implied volatility distribution. In- and out-of-sample, a linear CEV jump-diffusion model leads to valuation errors that are negligibly affected by the VIX options' maturity and moneyness. For this setup, we obtain parameter estimates that are comparable to the stock option pricing literature. Compared to a linear specification, we find that estimating the diffusion exponent freely does not lead to significantly better results.
Author : Asmerilda Hitaj
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (13 download)
Download or read book VIX Computation Based on Affine Stochastic Volatility Models in Discrete Time written by Asmerilda Hitaj and published by . This book was released on 2015 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. We build this class of models in order to reach two desirable results. Firstly, we have a recursive procedure for the characteristic function of the log price at maturity that allows a semi-analytical formula for option prices as in Heston and Nandi (2000). Secondly, we try to reproduce some features of the VIX Index. We derive a simple formula for the VIX index and use it for option pricing purposes.
Author : Pascal Marco Caversaccio
Publisher :
ISBN 13 :
Total Pages : 71 pages
Book Rating : 4.:/5 (13 download)
Download or read book Pricing VIX Options with Multifactor Stochastic Volatility written by Pascal Marco Caversaccio and published by . This book was released on 2016 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: By exploiting the flexibility of the Wishart process, we propose an application of this framework to the pricing of Chicago Board Options Exchange (CBOE) volatility index (VIX) options. Our methodology is analytically tractable and yet flexible enough to efficiently price CBOE VIX options. In particular, the dynamics for the CBOE VIX is carried out in a linear affine way and the discounted Laplace transform exhibits an exponentially affine property. The tractable model structure lightens the computational burden and facilitates a fast identification of the parameter estimates. We empirically show that modeling the stochastic co-volatility factor can significantly improve the in-sample fitting results due to the improved modeling of higher conditional moments in the underlying transition probability density.
Author : Juho Kanniainen
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (13 download)
Download or read book Estimating and Using GARCH Models with VIX Data for Option Valuation written by Juho Kanniainen and published by . This book was released on 2016 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper uses information on VIX to improve the empirical performance of GARCH models for pricing options on the S&P 500. In pricing multiple cross-sections of options, the models' performance can clearly be improved by extracting daily spot volatilities from the series of VIX rather than by linking spot volatility with different dates by using the series of the underlying's returns. Moreover, in contrast to traditional returns-based maximum likelihood estimation (MLE), a joint MLE with returns and VIX improves option pricing performance, and for NGARCH, joint MLE can yield empirically almost the same out-of-sample option pricing performance as direct calibration does to in-sample options, but without costly computations. Finally, consistently with the existing research, this paper finds that non-affine models clearly outperform affine models.
Author : Yue Kuen Kwok
Publisher : CRC Press
ISBN 13 : 1000584259
Total Pages : 283 pages
Book Rating : 4.0/5 (5 download)
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
Author : Martin Beck
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (781 download)
Download or read book Comparing the Hedging Performance of Affine Versus Non-Affine Option Pricing Models written by Martin Beck and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper compares the option hedging and pricing performance of affine and non-affine stochastic volatility (SV) models with and without jumps in returns on a set of S\&P 500 option data from 2005 to 2009. The squared volatility index VIX serves as a proxy for the latent spot variance process, model parameter estimates of Christoffersen, Jacobs and Mimouni (2010) are used and all experiments are out-of-sample tests. The evaluation of hedging performance is based on the distribution of hedging errors and their dependency on the underlying for daily and weekly hedge rebalancing and different hedging strategies: delta, minimum-variance and delta-vega hedging. Pricing performance is mainly assessed based on implied volatility root mean squared errors, and both pricing and hedging error measures are decomposed along various dimensions. Monte Carlo methods are used to compute option sensitivities and prices and the theoretical backgrounds of the option pricing models and applied methodologies are outlined in detail. Different conclusions hold for the hedging (dynamic) and pricing (static) performance of the SV models investigated. For hedging, all SV models perform relatively similar, underperforming a simple ad-hoc Black-Scholes hedge for delta hedging, but with better results for minimum-variance and delta-vega hedging. No non-affine model is consistently better than the affine Heston (1993) model for hedging. Pricing errors suggest that a non-affine GARCH-type model with linear variance diffusion and drift specification performs best along virtually all dimensions, and that the VIX is a good proxy for its filtered spot variance path. Jumps have minor effects on pricing performance and virtually no effect on hedging performance for all models. Considering both hedging and pricing performance, advantages of the best performing non-affine model need to be considered in conjunction with its lack of analytical tractability that impose.
Author : Alan L. Lewis
Publisher :
ISBN 13 : 9780967637211
Total Pages : 748 pages
Book Rating : 4.6/5 (372 download)
Download or read book Option Valuation Under Stochastic Volatility II written by Alan L. Lewis and published by . This book was released on 2016-05-12 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to the author's well-received "Option Valuation under Stochastic Volatility." It extends that work to jump-diffusions and many related topics in quantitative finance. Topics include spectral theory for jump-diffusions, boundary behavior for short-term interest rate models, modelling VIX options, inference theory, discrete dividends, and more. It provides approximately 750 pages of original research in 26 chapters, with 165 illustrations, Mathematica, and some C/C++ codes. The first 12 chapters (550 pages) are completely new. Also included are reprints of selected previous publications of the author for convenient reference. The book should interest both researchers and quantitatively-oriented investors and traders. First 12 chapters: Slow Reflection, Jump-Returns, & Short-term Interest Rates Spectral Theory for Jump-diffusions Joint Time Series Modelling of SPX and VIX Modelling VIX Options (and Futures) under Stochastic Volatility Stochastic Volatility as a Hidden Markov Model Continuous-time Inference: Mathematical Methods and Worked Examples A Closer Look at the Square-root and 3/2-model A Closer Look at the SABR Model Back to Basics: An Update on the Discrete Dividend Problem PDE Numerics without the Pain Exact Solution to Double Barrier Problems under a Class of Processes Advanced Smile Asymptotics: Geometry, Geodesics, and All That
Author : Frederik Knudsen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (19 download)
Download or read book Pricing SPX and VIX Options Jointly with Stochastic Volatility and Jump Models written by Frederik Knudsen and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Guanghua Lian
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Pricing Vix Options with Stochastic Volatility and Random Jumps written by Guanghua Lian and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study presents an analytical exact solution for the price of VIX options under stochastic volatility model with simultaneous jumps in the asset price and volatility processes. We shall demonstrate that our new pricing formula can be used to efficiently compute the numerical values of a VIX option. While we also show that the numerical results obtained from our formula consistently match those obtained from Monte Carlo simulation perfectly as a verification of the correctness of our formula, numerical evidence is offered to illustrate that the correctness of the formula proposed in Lin & Chang (2009) is in serious doubt. Moreover, some important and distinct properties of VIX options (e.g., put-call parity, hedging ratios) are also examined and discussed.
Author : José Da Fonseca
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (13 download)
Download or read book Analytic Pricing of Volatility-Equity Options Within Affine Models written by José Da Fonseca and published by . This book was released on 2015 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We price for different affine stochastic volatility models some derivatives that recently appeared in the market. These products are characterised by payoffs depending on both stock and its volatility. Using a Fourier-analysis approach, we recover in a much simpler way some results already established in the literature for the single factor specification of the volatility and we push forward our methodology, which turns out to be independent of the dimension of the problem, thanks to a simple conditioning with respect to the subfiltration generated by the variance path. For each product we provide a closed form solution based on the Fast Fourier Transform and we illustrate the results for realistic model parameter values. Also, our results highlight the great flexibility and tractability of the Wishart based stochastic volatility models.
Author : Li Kong
Publisher :
ISBN 13 : 9781124685823
Total Pages : 79 pages
Book Rating : 4.6/5 (858 download)
Download or read book Long Range Stochastic Volatility with Two Scales in Option Pricing written by Li Kong and published by . This book was released on 2012 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: We exploit a general framework, a martingale approach method, to estimate the derivative price for different stochastic volatility models. This method is a very useful tool for handling non-markovian volatility models. With this method, we get the order of the approximation error by evaluating the orders of three error correction terms. We also summarize some challenges in using the martingale approach method to evaluate the derivative prices. We propose two stochastic volatility models. Our goal is to get the analytical solution for the derivative prices implied by the models. Another goal is to obtain an explicit model for the implied volatility and in particular how it depends on time to maturity. The first model we propose involves the increments of a standard Brownian Motion for a short time increment. The second model involves fractional Brownian Motion(fBm) and two scales. By using fBm in our model, we naturally incorporate a long-range dependence feature of the volatility process. In addition, the implied volatility corresponding to our second model capture a feature of the volatility as observed in the paper Maturity cycles in implied volatility by Fouque, which analyzed the S & P 500 option price data and observed that for long dated options the implied volatility is approximately affine in the reciprocal of time to maturity, while for short dated options the implied volatility is approximately affine in the reciprocal of square root of time to maturity. The leading term in the implied volatility also matches the case when we have time-dependent volatility in the Black-Scholes equation.
Author : Yang-Ho Park
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (933 download)
Download or read book The Effects of Asymmetric Volatility and Jumps on the Pricing of VIX Derivatives written by Yang-Ho Park and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jacinto Marabel Romo
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (13 download)
Download or read book Pricing Volatility Options Under Stochastic Skew with Application to the VIX Index written by Jacinto Marabel Romo and published by . This book was released on 2015 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a remarkable growth of volatility options. In particular, VIX options are among the most actively trading contracts at CBOE. These options exhibit upward sloping volatility skew and the shape of the skew is largely independent of the volatility level. To take into account these stylized facts, this article introduces a novel two-factor stochastic volatility model with mean reversion that accounts for stochastic skew consistent with empirical evidence. Importantly, the model is analytically tractable. In this sense, I solve the pricing problem corresponding to standard-start, as well as to forward-start European options through the Fast Fourier Transform.To illustrate the practical performance of the model, I calibrate the model parameters to the quoted prices of European options on the VIX index. The calibration results are fairly good indicating the ability of the model to capture the shape of the implied volatility skew associated with VIX options.
Author : Lu Tian
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (799 download)
Download or read book Option Pricing Using Fourier Transformation Under Affine Stochastic Volatility Models written by Lu Tian and published by . This book was released on 2012 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lu Tian
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (84 download)
Download or read book Option Pricing Using Fourier Transform Under Affine Stochastic Volatility Models written by Lu Tian and published by . This book was released on 2012 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 73 pages
Book Rating : 4.:/5 (945 download)
Download or read book Consistent Pricing of SPX and VIX Options Using a Local-Stochastic Volatility Model with Heston Dynamics written by and published by . This book was released on 2015 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt:
