Affine Quadratic Jump Diffusion Term Structure Models
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| Author | : George J. Jiang |
| Publisher | : |
| Total Pages | : 41 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
In this paper, we propose a unifying affine-quadratic jump-diffusion framework for the term structure dynamics. The model incorporates both stochastic volatility and random jumps in the short rate process. In particular, we extend the existing models by explicitly modeling the jump intensity as a stochastic process. Using information from the treasury futures market, a GMM estimation approach is proposed for the risk-neutral process. A distinguishing feature of the approach is that the latent state variables are obtained, together with the model parameter estimates. The estimated latent state variables, namely the stochastic volatility and stochastic jump intensity, allow us to investigate the premia of various risk factors as well as underlying economic variables driving the term structure dynamics. Our empirical results suggest that the stochastic jump intensity significantly improves the model fit to the term structure dynamics. We identify a jump intensity negatively correlated with interest rate changes, a higher probability of positive jump than negative jump, and an on average larger size of negative jump than positive jump. We document a significant time-varying risk premium that is positively correlated with volatility.
| Author | : George J. Jiang |
| Publisher | : |
| Total Pages | : 13 |
| Release | : 2012 |
| Genre | : |
| ISBN | : |
In this paper, we propose a unifying class of affine-quadratic term structure models (AQTSMs) in the general jump-diffusion framework. Extending existing term structure models, the AQTSMs incorporate random jumps of stochastic intensity in the short rate process. Using information from the Treasury futures market, we propose a GMM approach for the estimation of the risk-neutral process. A distinguishing feature of the approach is that the time series estimates of stochastic volatility and jump intensity are obtained, together with model parameter estimates. Our empirical results suggest that stochastic jump intensity significantly improves the model fit to the term structure dynamics. We identify a stochastic jump intensity process that is negatively correlated with interest rate changes. Overall, negative jumps tend to have a larger size than positive ones. Our empirical results also suggest that, at monthly frequency, while stochastic volatility has certain predictive power of inflation, jumps are neither triggered by nor predictive of changes in macroeconomic variables. At daily frequency, however, we document interesting patterns for jumps associated with informational shocks in the financial market.
| Author | : Sanjay K. Nawalkha |
| Publisher | : John Wiley & Sons |
| Total Pages | : 722 |
| Release | : 2007-05-23 |
| Genre | : Business & Economics |
| ISBN | : 0470140062 |
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
| Author | : Damir Filipovic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 259 |
| Release | : 2009-07-28 |
| Genre | : Mathematics |
| ISBN | : 3540680152 |
Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.
| Author | : |
| Publisher | : |
| Total Pages | : |
| Release | : 2004 |
| Genre | : |
| ISBN | : |
We propose a multi-currency quadratic term structure model that allows for several sources of market incompleteness. A new feature of the model is the jump-quadratic dynamics of the exchange rates that simultaneously generate greater flexibility in the time-varying risk premium and excessive currency volatility. Our model empirically outperforms the complete market quadratic and affine multi-currency diffusion models. It accounts for the forward premium anomaly with reasonable market price of risks. The market incompleteness consists of idiosyncratic diffusion-like innovations and jump discontinuities. We find that the jumps dominate the variations in the currency returns and produce most of the excessive currency volatility.
| Author | : Daniel Alexandre Bloch |
| Publisher | : |
| Total Pages | : 42 |
| Release | : 2016 |
| Genre | : |
| ISBN | : |
Using the recent work of Alos and Ewald on option pricing approximations we extend their approach to some specific jump-diffusion models with stochastic interest rates, compute the Greeks and improve the accuracy of the approximations. Further, we obtain analytical solutions to the price of variance swap and volatility swap. Using these results we derive approximations to the equivalent implied volatility surface, and we relate the at-the-money forward term-structure of the surface when the correlation is set to zero to the volatility swap. To conclude we use in the FFT both a change of variable and the approximated call prices as control variates in the computation of more general jump-diffusion models, reducing the variance, making the call price square integrable and drastically increasing the speed of convergence.
| Author | : Koji Kusuda |
| Publisher | : |
| Total Pages | : 328 |
| Release | : 2003 |
| Genre | : |
| ISBN | : |
| Author | : Hao Zhou |
| Publisher | : |
| Total Pages | : 50 |
| Release | : 2001 |
| Genre | : Interest rates |
| ISBN | : |
| Author | : Hansjörg Albrecher |
| Publisher | : Walter de Gruyter |
| Total Pages | : 465 |
| Release | : 2009 |
| Genre | : Finance |
| ISBN | : 3110213133 |
Annotation This book is a collection of state-of-the-art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches. The volume is related to a a ~Special Semester on Stochastics with Emphasis on Financea (TM) that took place from September to December 2008 at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz, Austria
| Author | : Antonio Mele |
| Publisher | : MIT Press |
| Total Pages | : 1147 |
| Release | : 2022-11-22 |
| Genre | : Business & Economics |
| ISBN | : 0262046849 |
A comprehensive reference for financial economics, balancing theoretical explanations, empirical evidence, and the practical relevance of knowledge in the field. This volume offers a comprehensive, integrated treatment of financial economics, tracking the major milestones in the field and providing methodological tools. Doing so, it balances theoretical explanations, empirical evidence, and practical relevance. It illustrates nearly a century of theoretical advances with a vast array of models, showing how real phenomena (and, at times, market practice) have helped economists reformulate existing theories. Throughout, the book offers examples and solved problems that help readers understand the main lessons conveyed by the models analyzed. The book provides a unique and authoritative reference for the field of financial economics. Part I offers the foundations of the field, introducing asset evaluation, information problems in asset markets and corporate finance, and methods of statistical inference. Part II explains the main empirical facts and the challenges these pose for financial economists, which include excess price volatility, market liquidity, market dysfunctionalities, and the countercyclical behavior of market volatility. Part III covers the main instruments that protect institutions against the volatilities and uncertainties of capital markets described in part II. Doing so, it relies on models that have become the market standard, and incorporates practices that emerged from the 2007–2008 financial crisis.
