Effective Stochastic Volatility

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Effective Stochastic Volatility

Author : Mike Felpel
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Effective Stochastic Volatility by : Mike Felpel

Download or read book Effective Stochastic Volatility written by Mike Felpel and published by . This book was released on 2020 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are numerous models for specifying the uncertainty of future instantaneous volatility or variance, including the Heston, SABR and ZABR models. Often it is observed that a specific stochastic volatility model is chosen not for particular dynamical features, relevant for exotic payoff structures, but instead for convenience and ease of implementation. The SABR model, with its semi-closed form approximate solution for the prices of vanilla options, is a well-known example. In this article, we consider a general approach that includes all practically relevant stochastic volatility models and introduces new variants of the ZABR model. In particular, we consider the mean-reverting ZABR and free ZABR models. We use the method of deriving an effective partial differential equation for the density. This approach leads to the known approximation formula for the SABR model, but also provides expressions for arbitrage-free models. Numerical experiments illustrate our approach.

'Effective' Parameters for Stochastic Volatility Models

Author : Zaizhi Wang
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis 'Effective' Parameters for Stochastic Volatility Models by : Zaizhi Wang

Download or read book 'Effective' Parameters for Stochastic Volatility Models written by Zaizhi Wang and published by . This book was released on 2008 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper tackles the issue of approximated formula for stochastic model with time dependent model parameters, using an averaging principle. The idea lies in finding a similar model but with constant parameters that is the closest to our initial process, along the same lines as results proven by Gyouml;ngy (1986) for general stochastic processes. We extend previous results found by Piterbarg (2005) for the particular case of SABR model (Hagan (2002)). The resulting formula can be evaluated very quickly solving the implied Riccati equations. We compare the approximation with exact solution of the corresponding partial differential equation using an ADI method. Numerical results show that the approximation works well for short term maturities.

Effective Media Analysis for Stochastic Volatility Models

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (15 download)

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Book Synopsis Effective Media Analysis for Stochastic Volatility Models by :

Download or read book Effective Media Analysis for Stochastic Volatility Models written by and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Effective Methods for Generalized Stochastic Volatility Models

Author : Mike Oliver Felpel
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Effective Methods for Generalized Stochastic Volatility Models by : Mike Oliver Felpel

Download or read book Effective Methods for Generalized Stochastic Volatility Models written by Mike Oliver Felpel and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Volatility, the Effective Spread and Trading Activity

Author : Duy Tien Tran
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (154 download)

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Book Synopsis Stochastic Volatility, the Effective Spread and Trading Activity by : Duy Tien Tran

Download or read book Stochastic Volatility, the Effective Spread and Trading Activity written by Duy Tien Tran and published by . This book was released on 2007 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applications of efficient importance sampling to stochastic volatility models

Author : Serda Selin Ozturk
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Applications of efficient importance sampling to stochastic volatility models by : Serda Selin Ozturk

Download or read book Applications of efficient importance sampling to stochastic volatility models written by Serda Selin Ozturk and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Volatility Surface

Author : Jim Gatheral
Publisher : John Wiley & Sons
ISBN 13 : 1118046455
Total Pages : 204 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis The Volatility Surface by : Jim Gatheral

Download or read book The Volatility Surface written by Jim Gatheral and published by John Wiley & Sons. This book was released on 2011-03-10 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for The Volatility Surface "I'm thrilled by the appearance of Jim Gatheral's new book The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models--achieving remarkable clarity without giving up sophistication, depth, or breadth." --Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University "Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it." --Emanuel Derman, author of My Life as a Quant "Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form." --Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University "Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In The Volatility Surface he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility." --Paul Wilmott, author and mathematician "As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, The Volatility Surface gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it." --Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University "Jim Gatheral could not have written a better book." --Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP

Novel Methods in Computational Finance

Author : Matthias Ehrhardt
Publisher : Springer
ISBN 13 : 3319612824
Total Pages : 599 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Novel Methods in Computational Finance by : Matthias Ehrhardt

Download or read book Novel Methods in Computational Finance written by Matthias Ehrhardt and published by Springer. This book was released on 2017-09-19 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector. The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models. In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry. Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.

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.

Efficient Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method

Author : John L. Knight
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (154 download)

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Book Synopsis Efficient Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method by : John L. Knight

Download or read book Efficient Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method written by John L. Knight and published by . This book was released on 1999 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Volatility and Realized Stochastic Volatility Models

Author : Makoto Takahashi
Publisher : Springer Nature
ISBN 13 : 981990935X
Total Pages : 120 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Stochastic Volatility and Realized Stochastic Volatility Models by : Makoto Takahashi

Download or read book Stochastic Volatility and Realized Stochastic Volatility Models written by Makoto Takahashi and published by Springer Nature. This book was released on 2023-04-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.

Stochastic Volatility Option Pricing

Author : Nicolas Alain Jackson
Publisher :
ISBN 13 :
Total Pages : 83 pages
Book Rating : 4.:/5 (471 download)

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Book Synopsis Stochastic Volatility Option Pricing by : Nicolas Alain Jackson

Download or read book Stochastic Volatility Option Pricing written by Nicolas Alain Jackson and published by . This book was released on 1995 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Volatility Surface and Term Structure

Author : Kin Keung Lai
Publisher : Routledge
ISBN 13 : 1135006997
Total Pages : 102 pages
Book Rating : 4.1/5 (35 download)

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Book Synopsis Volatility Surface and Term Structure by : Kin Keung Lai

Download or read book Volatility Surface and Term Structure written by Kin Keung Lai and published by Routledge. This book was released on 2013-09-11 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.

Cross Sectional Efficient Estimation of Stochastic Volatility Short Rate Models

Author : D. Danilov
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (669 download)

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Book Synopsis Cross Sectional Efficient Estimation of Stochastic Volatility Short Rate Models by : D. Danilov

Download or read book Cross Sectional Efficient Estimation of Stochastic Volatility Short Rate Models written by D. Danilov and published by . This book was released on 2001 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Volatility

Author : Neil Shephard
Publisher : Oxford University Press, USA
ISBN 13 : 0199257205
Total Pages : 534 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Stochastic Volatility by : Neil Shephard

Download or read book Stochastic Volatility written by Neil Shephard and published by Oxford University Press, USA. This book was released on 2005 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This work brings together some of the main papers that have influenced this field, andshows that the development of this subject has been highly multidisciplinary.

Stochastic Volatility for Interest Rate Derivatives

Author : Linus Kaisajuntti
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Stochastic Volatility for Interest Rate Derivatives by : Linus Kaisajuntti

Download or read book Stochastic Volatility for Interest Rate Derivatives written by Linus Kaisajuntti and published by . This book was released on 2019 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper uses an extensive set of market data of forward swap rates and swaptions covering 3 July 2002 to 21 May 2009 to identify a two-dimensional stochastic volatility process for the level of rates. The process is identified step by step by increasing the requirement of the model and introduce appropriate adjustments.The first part of the paper investigates the smile dynamics of forward swap rates at their setting dates. Comparing the SABR (with different $ beta$s) and Heston stochastic volatility models informs about what different specifications of the driving SDEs has to offer in terms of reflecting the dynamics of the smile across dates. The outcome of the analysis is that a normal SABR model ($ beta=0$) satisfactorily passes all tests and seems to provide a good match to the market. In contrast we find the Heston model does not.The next step is to seek a model of the forward swap rates (in their own swaption measure) based on only two factors that enables a specification with common parameters. It turns out that this can be done by extending the SABR model with a time-dependent volatility function and a mean reverting volatility process. The performance of the extended (SABR with mean-reversion) model is analysed over several historical dates and is shown to be a stable and flexible choice that allows for good calibration across expiries and strikes. Finally a time-homogeneous candidate stochastic volatility process that can be used as a driver for all swap rates is identified and used to construct a simple terminal Markov-functional type model under a single measure. This candidate process may in future work be used as a building block for a separable stochastic volatility LIBOR market model or a stochastic volatility Markov-functional model.