Download or read book An Arbitrage Free Nelson Siegel Model with Unspanned Stochastic Volatility for the Pricing of Interest Rate Derivatives written by Rui Chen and published by . This book was released on 2014 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a generalized arbitrage-free Nelson-Siegel model under the HJM framework. It features unspanned stochastic volatility factors while maintaining a Nelson-Siegel factor loading structure. The price of the interest rate derivatives, including European options, Caps and Swaptions are then obtained in semi closed-form. We calibrate the model using an extensive panel data, including the US Libor rates, Swap rates, caps and swaptions. By estimating our model via the extended Kalman filter, we find strong evidence that our model prices interest rates and their derivatives accurately.
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 Issues in Finance Business and Economics Research 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Finance, Business, and Economics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Additional Research. The editors have built Issues in Finance, Business, and Economics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Additional Research in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Finance, Business, and Economics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Fixed Income Modelling written by Claus Munk and published by Oxford University Press. This book was released on 2011-06-30 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large number of securities related to various interest rates are traded in financial markets. Traders and analysts in the financial industry apply models based on economics, mathematics and probability theory to compute reasonable prices and risk measures for these securities. This book offers a unified presentation of such models and securities.
Download or read book Discrete Time Arbitrage Free Nelson Siegel Term Structure Model and Application written by Zhiwu Hong and published by . This book was released on 2016 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: We characterize the discrete-time arbitrage-free Nelson-Siegel term structure model, prove the uniqueness of the solution for model identification, make specification analysis on its canonical form, and detail the MCMC estimation method with a fast and reliable prior extraction step. Using the model, we examine how the yield curves of U.S. and China react to exchange rate policy shocks from China in its gradual reform to a more flexible exchange rate regime. Model decomposition reveals that, in U.S. yield responses, changes in risk premia for medium- to long-term yields dominate changes in yield expectation for short- to medium-term yields. The results are helpful to diagnosing market sentiment and exchange rate risk pricing as China further internationalizes its currency.
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 The Affine Arbitrage free Class of Nelson Siegel Term Structure Models written by Jens H. E. Christensen and published by . This book was released on 2007 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive the class of arbitrage-free affine dynamic term structure models that approximate the widely-used Nelson-Siegel yield-curve specification. Our theoretical analysis relates this new class of models to the canonical representation of the three-factor arbitrage-free affine model. Our empirical analysis shows that imposing the Nelson-Siegel structure on this canonical representation greatly improves its empirical tractability; furthermore, we find that improvements in predictive performance are achieved from the imposition of absence of arbitrage.
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 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.
Download or read book Handbook of Fixed Income Securities written by Pietro Veronesi and published by John Wiley & Sons. This book was released on 2016-04-04 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the current theories and methodologies intrinsic to fixed-income securities Written by well-known experts from a cross section of academia and finance, Handbook of Fixed-Income Securities features a compilation of the most up-to-date fixed-income securities techniques and methods. The book presents crucial topics of fixed income in an accessible and logical format. Emphasizing empirical research and real-life applications, the book explores a wide range of topics from the risk and return of fixed-income investments, to the impact of monetary policy on interest rates, to the post-crisis new regulatory landscape. Well organized to cover critical topics in fixed income, Handbook of Fixed-Income Securities is divided into eight main sections that feature: • An introduction to fixed-income markets such as Treasury bonds, inflation-protected securities, money markets, mortgage-backed securities, and the basic analytics that characterize them • Monetary policy and fixed-income markets, which highlight the recent empirical evidence on the central banks’ influence on interest rates, including the recent quantitative easing experiments • Interest rate risk measurement and management with a special focus on the most recent techniques and methodologies for asset-liability management under regulatory constraints • The predictability of bond returns with a critical discussion of the empirical evidence on time-varying bond risk premia, both in the United States and abroad, and their sources, such as liquidity and volatility • Advanced topics, with a focus on the most recent research on term structure models and econometrics, the dynamics of bond illiquidity, and the puzzling dynamics of stocks and bonds • Derivatives markets, including a detailed discussion of the new regulatory landscape after the financial crisis and an introduction to no-arbitrage derivatives pricing • Further topics on derivatives pricing that cover modern valuation techniques, such as Monte Carlo simulations, volatility surfaces, and no-arbitrage pricing with regulatory constraints • Corporate and sovereign bonds with a detailed discussion of the tools required to analyze default risk, the relevant empirical evidence, and a special focus on the recent sovereign crises A complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, Handbook of Fixed-Income Securities is also a useful supplementary textbook for graduate and MBA-level courses on fixed-income securities, risk management, volatility, bonds, derivatives, and financial markets. Pietro Veronesi, PhD, is Roman Family Professor of Finance at the University of Chicago Booth School of Business, where he teaches Masters and PhD-level courses in fixed income, risk management, and asset pricing. Published in leading academic journals and honored by numerous awards, his research focuses on stock and bond valuation, return predictability, bubbles and crashes, and the relation between asset prices and government policies.
Download or read book Libor Market Model with Stochastic Volatility written by Dariusz Gatarek and published by . This book was released on 2003 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Four papers introducing LIBOR market model (LMM) were published in 1997. They seemed to unify market practice with arbitrage-free framework - it came out that for one year only. The next year, after Russian crisis, cap and swaption markets started to show evident volatility smile and skew. Several attempts were made to capture that phenomenon into the arbitrage-free framework. Our note is strongly inspired by papers and conference talks by Mark Joshi and Riccardo Rebonato. We share their opinions that:- Since smiles and skews are caused by different market features, it is more natural to model smile and skew separately, rather then to use unified framework of implied smile.- Displaced Diffusion approach is easier in treatment then Constant Elasticity of Variance (CEV) approach for interest rate derivatives and gives the same modelling possibilities.- Displaced Diffusion and Stochastic Volatility are perfectly suited to work together.Since our attention is fixed more on swaptions then on caps/floors, we would like to opt for another version of the LIBOR market model with stochastic volatility and displaced diffusion (SVDDLMM) then Joshi and Rebonato:- We use various random displacement factors for various LIBOR rates. - For Stochastic Volatility we propose a new simple non mean reverting multi-lognormal model. We also try to convince the Reader that mean reversion in stochastic volatility models excludes correct modelling of long term options - swaptions are canonical example.Easy closed form formulae are given for caps/floors and European swaptions what makes calibration procedure more effective and transparent - at least we are not quot;prisoners of Monte Carloquot;. We are able to calibrate model to various smile/skew shapes for caps/floors and swaptions with various length and of various maturities.
Download or read book Arbitrage Free Valuation of Interest Rate Securities under Forward Curves with Stochastic Speed Acceleration written by Gurupdesh S. Pandher and published by . This book was released on 2011 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arbitrage-free models for valuing interest rate securities posit that stochastic changes in spot or forward interest rates (forward rate quot;speedquot;) follow a diffusion process. This paper extends the Heath, Jarrow and Morton (1992, HJM) framework by allowing diffusive shocks to both the quot;speedquot; and quot;accelerationquot; of forward rates. The arbitrage-free restriction on forward rates is identified and involves volatilities of the speed and acceleration dynamics and their correlation. Although the extended forward rates remain in the diffusive framework and evolve continuously, they may exhibit large changes over short intervals (as with jumps) due to stochastic acceleration. Comparisons of bond prices show that the proposed model generates more complex and intricate shapes for the restricted forward curve with the same number of stochastic factors and volatility.
Download or read book An Arbitrage free Generalized Nelson Siegel Term Structure Model written by Jens H. E. Christensen and published by . This book was released on 2008 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Svensson generalization of the popular Nelson-Siegel term structure model is widely used by practitioners and central banks. Unfortunately, like the original Nelson-Siegel specification, this generalization, in its dynamic form, does not enforce arbitrage-free consistency over time. Indeed, we show that the factor loadings of the Svensson generalization cannot be obtained in a standard finance arbitrage-free affine term structure representation. Therefore, we introduce a closely related generalized Nelson-Siegel model on which the no-arbitrage condition can be imposed. We estimate this new arbitrage-free generalized Nelson-Siegel model and demonstrate its tractability and good in-sample fit.
Download or read book An Arbitrage Free Generalized Nelson Siege Term Structure Model written by Jens Henrik Eggert Christensen and published by . This book was released on 2008 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Svensson generalization of the popular Nelson-Siegel term structure model is widely used by practitioners and central banks. Unfortunately, like the original Nelson-Siegel specification, this generalization, in its dynamic form, does not enforce arbitrage-free consistency over time. Indeed, we show that the factor loadings of the Svensson generalization cannot be obtained in a standard finance arbitrage-free affine term structure representation. Therefore, we introduce a closely related generalized Nelson-Siegel model on which the no-arbitrage condition can be imposed. We estimate this new arbitrage-free generalized Nelson-Siegel model and demonstrate its tractability and good in-sample fit.
Download or read book The Affine Arbitrage Free Class of written by Jens Henrik Eggert Christensen and published by . This book was released on 2010 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive the class of arbitrage-free affine dynamic term structure models that approximate the widely-used Nelson-Siegel yield-curve specification. Our theoretical analysis relates this new class of models to the canonical representation of the three-factor arbitrage-free affine model. Our empirical analysis shows that imposing the Nelson-Siegel structure on this canonical representation greatly improves its empirical tractability; furthermore, we find that improvements in predictive performance are achieved from the imposition of absence of arbitrage.
Download or read book How Arbitrage free is the Nelson Siegel Model written by Laura Coroneo and published by . This book was released on 2008 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Arbitrage Based Pricing When Volatility is Stochastic written by Peter Bossaerts and published by . This book was released on 2012 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: In one of the early attempts to model stochastic volatility, Clark [1973] conjectured that the size of asset price movements is tied to the rate at which transactions occur. To formally analyze the econometric implications, he distinguished between transaction time and calendar time. The present paper exploits Clark's strategy for a different purpose, namely, asset pricing. It studies arbitrage-based pricing in economies where: (i)trade takes place in transaction time, (ii) there is a single state variable whose transaction-time price path is binomial, (iii) there are riskfree bonds with calendar-time maturities, and (iv) the relation between transaction time and calendar time is stochastic. The state variable could be interpreted in various ways. E.g., it could be the price of a share of stock, as in Black and Scholes [1973], or a factor that summarizes changes in the investment opportunity set, as in Cox, Ingersoll and Ross [1985] or one that drives changes in the term structure of interest rates (Ho and Lee [1986], Heath, Jarrow and Morton [1992]). Property (iv) generally introduces stochastic volatility in the process of the state variable when recorded in calendar time.The paper investigates the pricing of derivative securities with calendar-time maturities. The restrictions obtained in Merton [1973] using simple buy-and-hold arbitrage portfolio arguments do not necessarily obtain. Conditions are derived for all derivatives to be priced by dynamic arbitrage, i.e., for market completeness in the sense of Harrison and Pliska [1981]. A particular class of stationary economies where markets are indeed complete is characterized.
