Long Range Stochastic Volatility With Two Scales In Option Pricing
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Long Range Stochastic Volatility With Two Scales In Option Pricing
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Author : Li Kong
language : en
Publisher:
Release Date : 2012
Long Range Stochastic Volatility With Two Scales In Option Pricing written by Li Kong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
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.
Option Pricing With Long Memory Stochastic Volatility Models
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Author : Zhigang Tong
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2013
Option Pricing With Long Memory Stochastic Volatility Models written by Zhigang Tong and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
It is now known that long memory stochastic volatility models can capture the well-documented evidence of volatility persistence. However, due to the complex structures of the long memory processes, the analytical formulas for option prices are not available yet. In this book, we propose two fractional continuous time stochastic volatility models which are built on the popular short memory stochastic volatility models. Using the tools from stochastic calculus, fractional calculus and Fourier transform, we derive the (approximate) analytical solutions for option prices. We also numerically study the effects of long memory on option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter. We also find that long memory models can accommodate the short term options and the decay of volatility skew better than the corresponding short memory models. These findings would appeal to the researchers and practitioners in the areas of quantitative finance.
Option Pricing With Long Memory Stochastic Volatility Models
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Author : Zhigang Tong
language : en
Publisher:
Release Date : 2012
Option Pricing With Long Memory Stochastic Volatility Models written by Zhigang Tong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Options (Finance) categories.
In this thesis, we propose two continuous time stochastic volatility models with long memory that generalize two existing models. More importantly, we provide analytical formulae that allow us to study option prices numerically, rather than by means of simulation. We are not aware about analytical results in continuous time long memory case. In both models, we allow for the non-zero correlation between the stochastic volatility and stock price processes. We numerically study the effects of long memory on the option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter in short memory models. We also find that long memory models have the potential to accommodate the short term options and the decay of volatility skew better than the corresponding short memory stochastic volatility models.
Complex Systems In Finance And Econometrics
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-03
Complex Systems In Finance And Econometrics written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-03 with Business & Economics categories.
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.
Modeling And Estimation Of Long Memory In Stochastic Volatility
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Author : Nazibrola Lordkipanidze
language : en
Publisher:
Release Date : 2004
Modeling And Estimation Of Long Memory In Stochastic Volatility written by Nazibrola Lordkipanidze and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Multiscale Stochastic Volatility For Equity Interest Rate And Credit Derivatives
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Author : Jean-Pierre Fouque
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-29
Multiscale Stochastic Volatility For Equity Interest Rate And Credit Derivatives written by Jean-Pierre Fouque and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-29 with Mathematics categories.
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
Stochastic Volatility Long Term Option And Discrete Time Problems In Fx
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Author : Francois-Stephane Robert Mantion
language : en
Publisher:
Release Date : 1998
Stochastic Volatility Long Term Option And Discrete Time Problems In Fx written by Francois-Stephane Robert Mantion and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Handbook Of Quantitative Finance And Risk Management
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Author : Cheng-Few Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-14
Handbook Of Quantitative Finance And Risk Management written by Cheng-Few Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-14 with Business & Economics categories.
Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This two-volume handbook, comprised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.
Stochastic Volatility And The Pricing Of Financial Derivatives
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Author : Antoine Petrus Cornelius van der Ploeg
language : en
Publisher: Rozenberg Publishers
Release Date : 2006
Stochastic Volatility And The Pricing Of Financial Derivatives written by Antoine Petrus Cornelius van der Ploeg and has been published by Rozenberg Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Mathematics Of Finance
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Author : George Yin
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Mathematics Of Finance written by George Yin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Business & Economics categories.
Contains papers based on talks given at the first AMS-IMS-SIAM Joint Summer Research Conference on Mathematics of Finance held at Snowbird. This book includes such topics as modeling, estimation, optimization, control, and risk assessment and management. It is suitable for students interested in mathematical finance.