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Author : Mthuli Ncube
Publisher :
ISBN 13 : 9783659241192
Total Pages : 124 pages
Book Rating : 4.2/5 (411 download)
Download or read book Jump Diffusion and Stochastic Volatility Models in Securities Pricing written by Mthuli Ncube and published by . This book was released on 2012 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Louis O. Scott
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (753 download)
Download or read book Pricing Stock Options in a Jump-diffusion Model with Stochastic Volatility and Interest Rates written by Louis O. Scott and published by . This book was released on 1995 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pascal Debus
Publisher : GRIN Verlag
ISBN 13 : 3656491941
Total Pages : 59 pages
Book Rating : 4.6/5 (564 download)
Download or read book Application of Stochastic Volatility Models in Option Pricing written by Pascal Debus and published by GRIN Verlag. This book was released on 2013-09-09 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bachelorarbeit aus dem Jahr 2010 im Fachbereich BWL - Investition und Finanzierung, Note: 1,2, EBS Universität für Wirtschaft und Recht, Sprache: Deutsch, Abstract: The Black-Scholes (or Black-Scholes-Merton) Model has become the standard model for the pricing of options and can surely be seen as one of the main reasons for the growth of the derivative market after the model ́s introduction in 1973. As a consequence, the inventors of the model, Robert Merton, Myron Scholes, and without doubt also Fischer Black, if he had not died in 1995, were awarded the Nobel prize for economics in 1997. The model, however, makes some strict assumptions that must hold true for accurate pricing of an option. The most important one is constant volatility, whereas empirical evidence shows that volatility is heteroscedastic. This leads to increased mispricing of options especially in the case of out of the money options as well as to a phenomenon known as volatility smile. As a consequence, researchers introduced various approaches to expand the model by allowing the volatility to be non-constant and to follow a sto-chastic process. It is the objective of this thesis to investigate if the pricing accuracy of the Black-Scholes model can be significantly improved by applying a stochastic volatility model.
Author : Daniel Janocha
Publisher : GRIN Verlag
ISBN 13 : 3656987599
Total Pages : 103 pages
Book Rating : 4.6/5 (569 download)
Download or read book Stochastic Modeling of Stock Prices Incorporating Jump Diffusion and Shot Noise Models written by Daniel Janocha and published by GRIN Verlag. This book was released on 2016-08-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master's Thesis from the year 2016 in the subject Mathematics - Stochastics, grade: 1,7, Technical University of Darmstadt (Forschungsgebiet Stochastik), course: Mathematik - Finanzmathematik, language: English, abstract: In this thesis, we present a stochastic model for stock prices incorporating jump diffusion and shot noise models based on the work of Altmann, Schmidt and Stute ("A Shot Noise Model For Financial Assets") and on its continuation by Schmidt and Stute ("Shot noise processes and the minimal martingale measure"). These papers differ in modeling the decay of the jump effect: Whereas it is deterministic in the first paper, it is stochastic in the last paper. In general, jump effects exist because of overreaction due to news in the press, due to illiquidity or due to incomplete information, i.e. because certain information are available only to few market participants. In financial markets, jump effects fade away as time passes: On the one hand, if the stock price falls, new investors are motivated to buy the stock. On the other hand, a rise of the stock price may lead to profit-taking, i.e. some investors sell the stock in order to lock in gains. Shot noise models are based on Merton's jump diffusion models where the decline of the jump effect after a price jump is neglected. In contrast to jump diffusion models, shot noise models respect the decay of jump effects. In complete markets, the so-called equivalent martingale measure is used to price European options and for hedging. Since stock price models incorporating jumps describe incomplete markets, the equivalent martingale measure cannot be determined uniquely. Hence, in this thesis, we deduce the so-called equivalent minimal martingale measure, both in discrete and continuous time. In contrast to Merton's jump diffusion models and to the well-known pricing model of Black and Scholes, the presented shot noise models are able to reproduce volatility smile effects which can be observed in financial markets.
Author : Abdelilah Jraifi
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659564895
Total Pages : 104 pages
Book Rating : 4.5/5 (648 download)
Download or read book Numerical Analysis Of Stochastic Volatility Jump Diffusion Models written by Abdelilah Jraifi and published by LAP Lambert Academic Publishing. This book was released on 2014-06-30 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern economic world, the options contracts are used because they allow to hedge against the vagaries and risks refers to fluctuations in the prices of the underlying assets. The determination of the price of these contracts is of great importance for investors.We are interested in problems of options pricing, actually the European and Quanto options on a financial asset. The price of that asset is modeled by a multi-dimentional jump diffusion with stochastic volatility. Otherwise, the first model considers the volatility as a continuous process and the second model considers it as a jump process. Finally in the 3rd model, the underlying asset is without jump and volatility follows a model CEV without jump. This model allow better to take into account some phenomena observed in the markets. We develop numerical methods that determine the values of prices for these options. We first write the model as an integro-differential stochastic equations system "EIDS," of which we study existence and unicity of solutions. Then we relate the resolution of PIDE to the computation of the option value.
Author : Aytekin Sari
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Stochastic Volatility and Jump Diffusion Option Pricing Model written by Aytekin Sari and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jim Gatheral
Publisher : John Wiley & Sons
ISBN 13 : 1118046455
Total Pages : 204 pages
Book Rating : 4.1/5 (18 download)
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
Author : Emanuel Derman
Publisher : John Wiley & Sons
ISBN 13 : 1118959175
Total Pages : 532 pages
Book Rating : 4.1/5 (189 download)
Download or read book The Volatility Smile written by Emanuel Derman and published by John Wiley & Sons. This book was released on 2016-08-15 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.
Author : Lei Zhang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (793 download)
Download or read book An Empirical Analysis of Jump Diffusion Stochastic Volatility Models for Currency Option Pricing written by Lei Zhang and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David S. Bates
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.:/5 (318 download)
Download or read book Jumps and Stochastic Volatility written by David S. Bates and published by . This book was released on 1993 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: An efficient method is developed for pricing American options on combination stochastic volatility/jump-diffusion processes when jump risk and volatility risk are systematic and nondiversifiable, thereby nesting two major option pricing models. The parameters implicit in PHLX-traded Deutschemark options of the stochastic volatility/jump- diffusion model and various submodels are estimated over 1984-91, and are tested for consistency with the $/DM futures process and the implicit volatility sample path. The parameters implicit in options are found to be inconsistent with the time series properties of implicit volatilities, but qualitatively consistent with log- differenced futures prices. No economically significant implicit expectations of exchange rate jumps were found in full-sample estimation, which is consistent with the reduced leptokurtosis of $/DM weekly exchange rate changes over 1984-91 relative to earlier periods.
Author : Peter Tankov
Publisher : CRC Press
ISBN 13 : 1135437947
Total Pages : 552 pages
Book Rating : 4.1/5 (354 download)
Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
Author : Desmond J. Higham
Publisher : Cambridge University Press
ISBN 13 : 1139457896
Total Pages : 300 pages
Book Rating : 4.1/5 (394 download)
Download or read book An Introduction to Financial Option Valuation written by Desmond J. Higham and published by Cambridge University Press. This book was released on 2004-04-15 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.
Author : Darrell Duffie
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 ( download)
Download or read book Transform Analysis and Asset Pricing for Affine Jump-diffusions written by Darrell Duffie and published by . This book was released on 1999 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the setting of affine' jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensityy-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option 'smirks' of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both amplitude as well as jump timing.
Author : Koji Kusuda
Publisher :
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.:/5 (319 download)
Download or read book Term Structure Models of Interest Rates with Jump-diffusion Information written by Koji Kusuda and published by . This book was released on 2003 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lorenzo Bergomi
Publisher : CRC Press
ISBN 13 : 1482244071
Total Pages : 520 pages
Book Rating : 4.4/5 (822 download)
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
Author : Yue Kuen Kwok
Publisher : CRC Press
ISBN 13 : 1000584275
Total Pages : 402 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 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
Author : Irena Andreevska
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (297 download)
Download or read book Mathematical Modeling and Analysis of Options with Jump-diffusion Volatility written by Irena Andreevska and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Several existing pricing models of financial derivatives as well as the effects of volatility risk are analyzed. A new option pricing model is proposed which assumes that stock price follows a diffusion process with square-root stochastic volatility. The volatility itself is mean-reverting and driven by both diffusion and compound Poisson process. These assumptions better reflect the randomness and the jumps that are readily apparent when the historical volatility data of any risky asset is graphed. The European option price is modeled by a homogeneous linear second-order partial differential equation with variable coefficients. The case of underlying assets that pay continuous dividends is considered and implemented in the model, which gives the capability of extending the results to American options. An American option price model is derived and given by a non-homogeneous linear second order partial integro-differential equation. Using Fourier and Laplace transforms an exact closed-form solution for the price formula for European call/put options is obtained.
