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A Stochastic Volatility Model And Inference For The Term Structure Of Interest
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Book Synopsis A Stochastic Volatility Model and Inference for the Term Structure of Interest Rates by : Peng Liu
Download or read book A Stochastic Volatility Model and Inference for the Term Structure of Interest Rates written by Peng Liu and published by . This book was released on 2007 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis builds a stochastic volatility model for the term structure of interest rates, which is also known as the dynamics of the yield curve. The main purpose of the model is to propose a parsimonious and plausible approach to capture some characteristics that conform to some empirical evidence and conventions. Eventually, the development reaches a class of multivariate stochastic volatility models, which is flexible, extensible, providing the existence of an inexpensive inference approach.
Book Synopsis A Stochastic Volatility Model and Inference for the Term Structure of Interest by :
Download or read book A Stochastic Volatility Model and Inference for the Term Structure of Interest written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis builds a stochastic volatility model for the term structure of interest rates, which is also known as the dynamics of the yield curve. The main purpose of the model is to propose a parsimonious and plausible approach to capture some characteristics that conform to some empirical evidences and conventions. Eventually, the development reaches a class of multivariate stochastic volatility models, which is flexible, extensible, providing the existence of an inexpensive inference approach. The thesis points out some inconsistency among conventions and practice. First, yield curves and its related curves are conventionally smooth. But in the literature that these curves are modeled as random functions, the co-movement of points on the curve are usually assumed to be governed by some covariance structures that do not generate smooth random curves. Second, it is commonly agreed that the constant volatility is not a sound assumption, but stochastic volatilities have not been commonly considered in related studies. Regarding the above problems, we propose a multiplicative factor stochastic volatility model, which has a relatively simple structure. Though it is apparently simple, the inference is not, because of the presence of stochastic volatilities. We first study the sequential-Monte-Carlo-based maximum likelihood approach, which extends the perspectives of Gaussian linear state-space modeling. We propose a systematic procedure that guides the inference based on this approach. In addition, we also propose a saddlepoint approximation approach, which integrates out states. Then the state propagates by an exact Gaussian approximation. The approximation works reasonably well for univariate models. Moreover, it works even better for the multivariate model that we propose. Because we can enjoy the asymptotic property of the saddlepoint approximation.
Book Synopsis A Class of Stochastic Volatility Models for the Term Structure of Interest Rates by : Elisa Nicolato
Download or read book A Class of Stochastic Volatility Models for the Term Structure of Interest Rates written by Elisa Nicolato and published by . This book was released on 1999 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Volatility in Financial Markets by : Antonio Mele
Download or read book Stochastic Volatility in Financial Markets written by Antonio Mele and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Volatility in Financial Markets presents advanced topics in financial econometrics and theoretical finance, and is divided into three main parts. The first part aims at documenting an empirical regularity of financial price changes: the occurrence of sudden and persistent changes of financial markets volatility. This phenomenon, technically termed `stochastic volatility', or `conditional heteroskedasticity', has been well known for at least 20 years; in this part, further, useful theoretical properties of conditionally heteroskedastic models are uncovered. The second part goes beyond the statistical aspects of stochastic volatility models: it constructs and uses new fully articulated, theoretically-sounded financial asset pricing models that allow for the presence of conditional heteroskedasticity. The third part shows how the inclusion of the statistical aspects of stochastic volatility in a rigorous economic scheme can be faced from an empirical standpoint.
Book Synopsis Unspanned Stochastic Volatility Term Structure Model Applied in Negative Interest Rate Environment by : Jan Sedlak
Download or read book Unspanned Stochastic Volatility Term Structure Model Applied in Negative Interest Rate Environment written by Jan Sedlak and published by . This book was released on 2016 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest rate transition from the positive environment, into the negative territory questions the consensus of interest rates and opens up a wide field of unresearched areas. To cope with the changing interest rate environment as well as satisfying regulatory criteria, a model following the Heath-Jarrow-Morton framework with Unspanned Stochastic Volatility is implemented. The model is constructed to match shocks to the level, slope and curvature of the term structure. Estimation is performed with Libor rates, Government rates and Swaption ATM normal implied volatilities from 2006-01-01 to 2015-03-12. The model is backtested both in sample and out of sample and compared to a Normal model and a Log Normal model. The model shows a good quantile fit to the medium and long end of the term structure and performs relatively better then the two challenger models.
Book Synopsis A Simple Approach to the Estimation of Continuous Time CEV Stochastic Volatility Models of the Short-term Rate by : Fabio Fornari
Download or read book A Simple Approach to the Estimation of Continuous Time CEV Stochastic Volatility Models of the Short-term Rate written by Fabio Fornari and published by . This book was released on 2001 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Mean and Stochastic Volatility by : Lin Chen
Download or read book Stochastic Mean and Stochastic Volatility written by Lin Chen and published by . This book was released on 1996 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modelling and forecasting stock return volatility and the term structure of interest rates by : Michiel de Pooter
Download or read book Modelling and forecasting stock return volatility and the term structure of interest rates written by Michiel de Pooter and published by Rozenberg Publishers. This book was released on 2007 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of a collection of studies on two areas in quantitative finance: asset return volatility and the term structure of interest rates. The first part of this dissertation offers contributions to the literature on how to test for sudden changes in unconditional volatility, on modelling realized volatility and on the choice of optimal sampling frequencies for intraday returns. The emphasis in the second part of this dissertation is on the term structure of interest rates.
Book Synopsis A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives by : Anders B. Trolle
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 2006 with total page 62 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.
Book Synopsis Uncertain Volatility Models by : Robert Buff
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.
Book Synopsis Stochastic Mean and Stochastic Volatility by : Lin Chen
Download or read book Stochastic Mean and Stochastic Volatility written by Lin Chen and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper a three-factor model of the term structure of interest rates is developed. In the model the future short rate depends on 1) the current short rate, 2) the short-term mean of the short rate, and 3) the current volatility of the short rate. Furthermore, it is assumed that both the short term mean of the short rate and the volatility of the short rate are stochastic and follow square-root process. The model is a substantial extension the seminal Cox-Ingersoll-Ross model of interest rates. A general formula for evaluating interest rate derivatives is presented. Closed-form solutions for prices of bond, bond option, futures, futures option, swap and cap are derived. The model can fit into the Heath-Jarrow-Morton arbitrage framework. The model is also useful for other practical purposes such as managing interest rate risks and formulating fixed income arbitrage strategies.
Book Synopsis A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives by : Anders B. Trolle
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.
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.
Book Synopsis Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives by : Jean-Pierre Fouque
Download or read book Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2011-09-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Handbook of Volatility Models and Their Applications by : Luc Bauwens
Download or read book Handbook of Volatility Models and Their Applications written by Luc Bauwens and published by John Wiley & Sons. This book was released on 2012-03-22 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.
Book Synopsis Term Structure and Volatility by : Ruslan Bikbov
Download or read book Term Structure and Volatility written by Ruslan Bikbov and published by . This book was released on 2004 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: We evaluate the ability of several affine models to explain the term structure of the interest rates and option prices. Since the key distinguishing characteristic of the affine models is the specification of conditional volatility of the factors, we explore models which have critical differences in this respect: Gaussian (constant volatility), stochastic volatility, and unspanned stochastic volatility models. We estimate the models based on the Eurodollar futures and options data. We find that both Gaussian and stochastic volatility models, despite the differences in the specifications, do a great job matching the conditional mean and volatility of the term structure. When these models are estimated using options data, their properties change, and they are more successful in pricing options and matching higher moments of the term structure distribution. The unspanned stochastic volatility (USV) model fails to resolve the tension between the futures and options fits. Unresolved tension in the fits points to additional factors or, even more likely, jumps, as ways to improve the performance of the models. Our results indicate that Gaussian and stochastic volatility models cannot be distinguished based on the yield curve dynamics alone. Options data are helpful in identifying the differences. In particular, Gaussian models cannot explain the relationship between implied volatilities and the term structure observed in the data.
Book Synopsis Analytical Solutions of the SABR Stochastic Volatility Model by : Qi Wu
Download or read book Analytical Solutions of the SABR Stochastic Volatility Model written by Qi Wu and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Our empirical studies extend the forward concept from interest rate term structure modeling to interest rate volatility term structure modeling and examine the relationship between today's forward implied volatility and future spot implied volatility.
