Download or read book Unspanned Stochastic Volatility in the Multi Factor CIR Model written by Damir Filipovic and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Download or read book A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives written by Anders B. Trolle and published by . This book was released on 2016 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features unspanned stochastic volatility factors, correlation between innovations to forward rates and their volatilities, quasi-analytical prices of zero-coupon bond options, and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finitedimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities.

Download or read book Spanned Stochastic Volatility in Bond Markets written by Don H. Kim and published by . This book was released on 2007 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper reexamines the issue of unspanned stochastic volatility (USV) in bond markets and the puzzle of poor relative pricing between bonds and bond options. I make a distinction between the "weak USV" and the "strong USV" scenarios, and analyze the evidence for each of them. I argue that the poor bonds/options relative pricing in the extant literature is not necessarily evidence for the strong USV scenario, and show that a maximally flexible 2-factor quadratic-Gaussian model (a non-USV model) estimated without bond options data can capture much of the movement in bond option prices. Dropping the positive-definiteness requirement for nominal interest rates and adopting "regularized" estimations turn out to be important for obtaining sensible results.

Download or read book Exact Solution to CEV Model with Uncorrelated Stochastic Volatility written by Alexandre Antonov and published by . This book was released on 2014 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility models are widely used in interest rate modeling to match the option smiles -- the two most popular are the Heston model and the SABR one. These have been incorporated into arbitrage-free term structure frameworks, Heston-LMM and SABR-LMM respectively.In this paper we consider the CEV model with a general stochastic volatility. Assuming that rate-volatility correlation is zero we are able to obtain an exact integral representation of the option price provided that we have a closed form for a Moment Generating Function of the cumulative stochastic variance or of its inverse. Using this result we derive explicit solutions in terms of two-dimensional integral for both CEV-CIR model (or power generalization of the Heston) and the SABR one. Moreover the results in this paper may be easily extended to any affine process (possibly multi-factor and including jumps) leading to numerous practical applications.

Download or read book A Multi factor Quadratic Stochastic Volatility Model with Applications in Finance and Insurance written by Michail Korniotis and published by . This book was released on 2009 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a multi-factor stochastic model that can be used as a modeling tool in several areas of applied mathematics. Our modeling efforts are focused on addressing the basic characteristics of quantities that represent random rate of change. These characteristics include properties of their evolution pattern, cross-factor correlation, and the stochastic nature of their diffusion parameter. At the same time, we address the question of solutions implied by the model, as well as the model's tractability. The model is introduced in a general mathematical context, prior to any specific problem consideration. We choose this approach to stress the model's functional independence of any particular application. Within this framework, we are able to represent the evolution of quantities sensitive to random rates of change, as solutions of partial differential equations. We obtain solutions of the resulting partial differential equations by adopting a two-step solution method. The first step approximates the solution using perturbation methods. This procedure specifies the two leading terms as solutions of simpler differential problems. The second step allows us to derive explicit solutions for the terms using the eigenfunction expansion method. A computer algorithm for the solution was also built. This allowed the calibration of the model parameters and a comparison of fitness with existing models. The usefulness and flexibility of the model is demonstrated by considering applications in three areas of applied mathematics: Interest rate, credit risk, and mortality modeling. We comment on how our model generalizes existing models in these areas and its advantages over previously proposed models.

Download or read book A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives written by Anders B. Trolle and published by . This book was released on 2010 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasi-analytical prices of zero-coupon bond options and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finite-dimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives.

Download or read book Handbook of Computational Finance written by Jin-Chuan Duan and published by Springer Science & Business Media. This book was released on 2011-10-25 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.

Download or read book A Dual Curve Short Rate Model with Multi Factor Stochastic Volatility written by Andrew Lesniewski and published by . This book was released on 2016 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a stochastic-volatility, short rate term structure model, which extends the classic multi-factor Hull-White model. This model is designed to fit the swaption implied volatility cube and to incorporate the two-curve modeling paradigm. The model exhibits non-Gaussian forward swap rates whose distributions are parameterized across the dimensions of the volatility cube: underlying tenor, option strike and option expiration. To facilitate rapid model calibration, we establish suitable asymptotic expressions for the bond prices. Furthermore, we derive an effective SABR dynamics for each forward swap rate. Finally, we use the mean field approximation to match the effective SABR parameters corresponding to each swaption to the market levels.

Download or read book A Maximal Stochastic Volatility Model for Commodity Prices written by Walker Keener Hughen and published by . This book was released on 2007 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamic Term Structure Modeling written by Sanjay K. Nawalkha and published by John Wiley & Sons. This book was released on 2007-05-23 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling

Download or read book Stochastic Volatility for Real written by Jesper Andreasen and published by . This book was released on 2006 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: We combine classical ideas of separable volatility structures in the HJM framework with the latest techniques for calibration of stochastic volatility models and create a new class of efficient multi-factor term structure models with stochastic volatility. These models have the flexibility of as the Libor market models but the speed of the short rate models.

Download or read book Handbook of Quantitative Finance and Risk Management written by Cheng-Few Lee and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 1700 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Explicit Implied Volatilities for Multifactor Local Stochastic Volatility Models written by Matthew Lorig and published by . This book was released on 2014 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under five different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility, 3/2 stochastic volatility, and SABR local-stochastic volatility.

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:

Download or read book Uncertain Volatility Models written by Robert Buff and published by Springer Science & Business Media. This book was released on 2002-04-10 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.

Download or read book Pricing of Bond Options written by Detlef Repplinger and published by Springer Science & Business Media. This book was released on 2008-08-15 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: A major theme of this book is the development of a consistent unified model framework for the evaluation of bond options. In general options on zero bonds (e.g. caps) and options on coupon bearing bonds (e.g. swaptions) are linked by no-arbitrage relations through the correlation structure of interest rates. Therefore, unspanned stochastic volatility (USV) as well as Random Field (RF) models are used to model the dynamics of entire yield curves. The USV models postulate a correlation between the bond price dynamics and the subordinated stochastic volatility process, whereas Random Field models allow for a deterministic correlation structure between bond prices of different terms. Then the pricing of bond options is done either by running a Fractional Fourier Transform or by applying the Integrated Edgeworth Expansion approach. The latter is a new extension of a generalized series expansion of the (log) characteristic function, especially adapted for the computation of exercise probabilities.