Modelling Stochastic Volatility With Leverage And Jumps

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Modelling Stochastic Volatility with Leverage and Jumps

Author : Sheheryar Malik
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Modelling Stochastic Volatility with Leverage and Jumps by : Sheheryar Malik

Download or read book Modelling Stochastic Volatility with Leverage and Jumps written by Sheheryar Malik and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we provide a unified methodology for conducting likelihood-based inference on the unknown parameters of a general class of discrete-time stochastic volatility (SV) models, characterized by both a leverage effect and jumps in returns. Given the nonlinear/non-Gaussian state-space form, approximating the likelihood for the parameters is conducted with output generated by the particle filter. Methods are employed to ensure that the approximating likelihood is continuous as a function of the unknown parameters thus enabling the use of standard Newton-Raphson type maximization algorithms. Our approach is robust and efficient relative to alternative Markov Chain Monte Carlo schemes employed in such contexts. In addition it provides a feasible basis for undertaking the nontrivial task of model comparison. Furthermore, we introduce new volatility model, namely SV-GARCH which attempts to bridge the gap between GARCH and stochastic volatility specifications. In nesting the standard GARCH model as a special case, it has the attractive feature of inheriting the same unconditional properties of the standard GARCH model but being conditionally heavier-tailed; thus more robust to outliers. It is demonstrated how this model can be estimated using the described methodology. The technique is applied to daily returns data for S&P 500 stock price index for various spans. In assessing the relative performance of SV with leverage and jumps and nested specifications, we find strong evidence in favour of a including leverage effect and jumps when modelling stochastic volatility. Additionally, we find very encouraging results for SV-GARCH in terms of predictive ability which is comparable to the other models considered.

EGARCH and Stochastic Volatility

Author : Jouchi Nakajima
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis EGARCH and Stochastic Volatility by : Jouchi Nakajima

Download or read book EGARCH and Stochastic Volatility written by Jouchi Nakajima and published by . This book was released on 2008 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This paper proposes the EGARCH [Exponential Generalized Autoregressive Conditional Heteroskedasticity] model with jumps and heavy-tailed errors, and studies the empirical performance of different models including the stochastic volatility models with leverage, jumps and heavy-tailed errors for daily stock returns. In the framework of a Bayesian inference, the Markov chain Monte Carlo estimation methods for these models are illustrated with a simulation study. The model comparison based on the marginal likelihood estimation is provided with data on the U.S. stock index."--Author's abstract.

Discrete-time Volatility Forecasting with Persistent Leverage Effect and the Link with Continuous-time Volatility Modeling

Author : Fulvio Corsi
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Discrete-time Volatility Forecasting with Persistent Leverage Effect and the Link with Continuous-time Volatility Modeling by : Fulvio Corsi

Download or read book Discrete-time Volatility Forecasting with Persistent Leverage Effect and the Link with Continuous-time Volatility Modeling written by Fulvio Corsi and published by . This book was released on 2010 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We first propose a reduced-form model in discrete time for Samp;P500 volatility showing that the forecasting performance of a volatility model can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly. We then estimate continuous-time stochastic volatility models which are able to reproduce the statistical features captured by the reduced-form model. We show that a single-factor model driven by a fractional Brownian motion is unable to reproduce the volatility dynamics observed in the data, while a multi-factor Markovian model is able to reproduce the persistence of both volatility and leverage effect. The impact of jumps can instead be associated with a common jump component in price and volatility. These findings cast serious doubts on the need of modeling volatility with a genuine long memory component, while reinforcing the view of volatility being generated by the superposition of multiple factors.

Beyond Stochastic Volatility and Jumps in Returns and Volatility

Author : Garland Durham
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Beyond Stochastic Volatility and Jumps in Returns and Volatility by : Garland Durham

Download or read book Beyond Stochastic Volatility and Jumps in Returns and Volatility written by Garland Durham and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: While a great deal of attention has been focused on stochastic volatility in stock returns, there is strong evidence suggesting that return distributions have time-varying skewness and kurtosis as well. Under the risk-neutral measure, for example, this can be seen from variation across time in the shape of Black-Scholes implied volatility smiles. This paper investigates model characteristics that are consistent with variation in the shape of return distributions using a stochastic volatility model with a regime-switching feature to allow for random changes in the parameters governing volatility of volatility, leverage effect and jump intensity. The analysis consists of two steps. First, the models are estimated using only information from observed returns and option-implied volatility. Standard model assessment tools indicate a strong preference in favor of the proposed models. Since the information from option-implied skewness and kurtosis is not used in fitting the models, it is available for diagnostic purposes. In the second step of the analysis, regressions of option-implied skewness and kurtosis on the filtered state variables (and some controls) suggest that the models have strong explanatory power for these characteristics.

On Leverage in a Stochastic Volatility Model

Author : Jun Yu
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (224 download)

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Book Synopsis On Leverage in a Stochastic Volatility Model by : Jun Yu

Download or read book On Leverage in a Stochastic Volatility Model written by Jun Yu and published by . This book was released on 2004 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with specification for modelling finanical leverage effect in the context of stochastic volatility models.

Stochastic Volatility Modeling

Author : Lorenzo Bergomi
Publisher : CRC Press
ISBN 13 : 1482244071
Total Pages : 520 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Stochastic Volatility Modeling by : Lorenzo Bergomi

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by CRC Press. This book was released on 2015-12-16 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c

The Estimation of Stochastic Models in Finance with Volatility and Jump Intensity

Author : David Edward A. Wilson
Publisher :
ISBN 13 :
Total Pages : 365 pages
Book Rating : 4.:/5 (19 download)

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Book Synopsis The Estimation of Stochastic Models in Finance with Volatility and Jump Intensity by : David Edward A. Wilson

Download or read book The Estimation of Stochastic Models in Finance with Volatility and Jump Intensity written by David Edward A. Wilson and published by . This book was released on 2018 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis covers the parametric estimation of models with stochastic volatility, jumps, and stochastic jump intensity, by FFT. The first primary contribution is a parametric minimum relative entropy optimal Q-measure for affine stochastic volatility jump-diffusion (ASVJD). Other attempts in the literature have minimized the relative entropy of Q given P either by nonparametric methods, or by numerical PDEs. These methods are often difficult to implement. We construct the relative entropy of Q given P from the Lebesgue densities under P and Q, respectively, where these can be retrieved by FFT from the closed form log-price characteristic function of any ASVJD model. We proceed by first estimating the fixed parameters of the P-measure by the Approximate Maximum Likelihood (AML) method of Bates (2006), and prove that the integrability conditions required for Fourier inversion are satisfied. Then by using a structure preserving parametric model under the Q-measure, we minimize the relative entropy of Q given P with respect to the model parameters under Q. AML can be used to estimate P within the ASVJD class. Since, AML is much faster than MCMC, our main supporting contributions are to the theory of AML. The second main contribution of this thesis is a non-affine model for time changed jumps with stochastic jump intensity called the Leveraged Jump Intensity (LJI) model. The jump intensity in the LJI model is modeled by the CIR process. Leverage occurs in the LJI model, since the Brownian motion driving the CIR process also appears in the log-price with a negative coefficient. Models with a leverage effect of this type are usually affine, but model the intensity with an Ornstein-Uhlenbeck process. The conditional characteristic function of the LJI log-price given the intensity is known in closed form. Thus, we price LJI call options by conditional Monte Carlo, using the Carr and Madan (1999) FFT formula for conditional pricing.

Research Report

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (912 download)

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Book Synopsis Research Report by :

Download or read book Research Report written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Discrete-Time Model for Daily S&P 500 Returns and Realized Variations

Author : Tim Bollerslev
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis A Discrete-Time Model for Daily S&P 500 Returns and Realized Variations by : Tim Bollerslev

Download or read book A Discrete-Time Model for Daily S&P 500 Returns and Realized Variations written by Tim Bollerslev and published by . This book was released on 2008 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuous-time components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easy-to-implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and Levy-driven stochastic volatility models, effectively incorporating the relevant information in the high-frequency data.

Stochastic Volatility Model with Jumps in Returns and Volatility

Author : Adjoa K. Numatsi
Publisher :
ISBN 13 :
Total Pages : 258 pages
Book Rating : 4.:/5 (78 download)

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Book Synopsis Stochastic Volatility Model with Jumps in Returns and Volatility by : Adjoa K. Numatsi

Download or read book Stochastic Volatility Model with Jumps in Returns and Volatility written by Adjoa K. Numatsi and published by . This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Simulation Methods for Levy-Driven Carma Stochastic Volatility Models

Author : George Tauchen
Publisher :
ISBN 13 :
Total Pages : 41 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Simulation Methods for Levy-Driven Carma Stochastic Volatility Models by : George Tauchen

Download or read book Simulation Methods for Levy-Driven Carma Stochastic Volatility Models written by George Tauchen and published by . This book was released on 2008 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop simulation schemes for the new classes of non-Gaussian pure jump Levy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Levy process, which then makes series approximation methods directly applicable. These methods entail simulation of the Levy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function nor specification of a copula function. We also present a new, and apparently quite flexible, bivariate mixture of gammas model for the driving Levy process. Within this setup, it is quite straightforward to generate simulations from a Levy-driven CARMA stochastic volatility model augmented by a pure-jump price component. Simulations reveal the wide range of different types of financial price processes that can be generated in this manner, including processes with persistent stochastic volatility, dynamic leverage, and jumps.

A Stochastic Volatility Model with Leverage Effect and Regime Switching

Author : Hong Jiang
Publisher :
ISBN 13 :
Total Pages : 125 pages
Book Rating : 4.:/5 (915 download)

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Book Synopsis A Stochastic Volatility Model with Leverage Effect and Regime Switching by : Hong Jiang

Download or read book A Stochastic Volatility Model with Leverage Effect and Regime Switching written by Hong Jiang and published by . This book was released on 2014 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A New Class of Stochastic Volatility Models with Jumps : Theory and Estimation

Author : CIRANO.
Publisher : Montréal : CIRANO
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (442 download)

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Book Synopsis A New Class of Stochastic Volatility Models with Jumps : Theory and Estimation by : CIRANO.

Download or read book A New Class of Stochastic Volatility Models with Jumps : Theory and Estimation written by CIRANO. and published by Montréal : CIRANO. This book was released on 1999 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Study About the Existence of the Leverage Effect in Stochastic Volatility Models

Author : Ionut Florescu
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis A Study About the Existence of the Leverage Effect in Stochastic Volatility Models by : Ionut Florescu

Download or read book A Study About the Existence of the Leverage Effect in Stochastic Volatility Models written by Ionut Florescu and published by . This book was released on 2018 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: The empirical relationship between the return of an asset and the volatility of the asset has been well documented in the financial literature. Named the leverage e ffect or sometimes risk-premium effect, it is observed in real data that, when the return of the asset decreases, the volatility increases and vice-versa.Consequently, it is important to demonstrate that any formulated model for the asset price is capable to generate this eff ect observed in practice. Furthermore, we need to understand the conditions on the parameters present in the model that guarantee the apparition of the leverage effect. In this paper we analyze two general speci cations of stochastic volatility models and their capability of generating the perceived leverage effect. We derive conditions for the apparition of leverage e ffect in both of these stochastic volatility models. We exemplify using stochastic volatility models used in practice and we explicitly state the conditions for the existence of the leverage effect in these examples.

Stochastic volatility and the pricing of financial derivatives

Author : Antoine Petrus Cornelius van der Ploeg
Publisher : Rozenberg Publishers
ISBN 13 : 9051705778
Total Pages : 358 pages
Book Rating : 4.0/5 (517 download)

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Book Synopsis Stochastic volatility and the pricing of financial derivatives by : Antoine Petrus Cornelius van der Ploeg

Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Systems in Finance and Econometrics

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1441977007
Total Pages : 919 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Complex Systems in Finance and Econometrics by : Robert A. Meyers

Download or read book Complex Systems in Finance and Econometrics written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finance, Econometrics and System Dynamics presents an overview of the concepts and tools for analyzing complex systems in a wide range of fields. The text integrates complexity with deterministic equations and concepts from real world examples, and appeals to a broad audience.

Nonparametric Statistical Methods

Author : Myles Hollander
Publisher : John Wiley & Sons
ISBN 13 : 1118553292
Total Pages : 872 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Nonparametric Statistical Methods by : Myles Hollander

Download or read book Nonparametric Statistical Methods written by Myles Hollander and published by John Wiley & Sons. This book was released on 2013-11-25 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition “This book should be an essential part of the personal library of every practicing statistician.”—Technometrics Thoroughly revised and updated, the new edition of Nonparametric Statistical Methods includes additional modern topics and procedures, more practical data sets, and new problems from real-life situations. The book continues to emphasize the importance of nonparametric methods as a significant branch of modern statistics and equips readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for any given situation. Written by leading statisticians, Nonparametric Statistical Methods, Third Edition provides readers with crucial nonparametric techniques in a variety of settings, emphasizing the assumptions underlying the methods. The book provides an extensive array of examples that clearly illustrate how to use nonparametric approaches for handling one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. In addition, the Third Edition features: The use of the freely available R software to aid in computation and simulation, including many new R programs written explicitly for this new edition New chapters that address density estimation, wavelets, smoothing, ranked set sampling, and Bayesian nonparametrics Problems that illustrate examples from agricultural science, astronomy, biology, criminology, education, engineering, environmental science, geology, home economics, medicine, oceanography, physics, psychology, sociology, and space science Nonparametric Statistical Methods, Third Edition is an excellent reference for applied statisticians and practitioners who seek a review of nonparametric methods and their relevant applications. The book is also an ideal textbook for upper-undergraduate and first-year graduate courses in applied nonparametric statistics.