Park, F. C., Chun, C. M., Han, C. W. and Webber, Nick. (2011) Interest rate models on lie groups. Quantitative Finance, Vol.11 (No.4). pp. 559-572. ISSN 1469-7688

Full text not available from this repository.

Abstract

This paper examines an alternative approach to interest rate modeling, in which the nonlinear and random behavior of interest rates is captured by a stochastic differential equation evolving on a curved state space. We consider as candidate state spaces the matrix Lie groups; these offer not only a rich geometric structure, butunlike general Riemannian manifoldsalso allow for diffusion processes to be constructed easily without invoking the machinery of stochastic calculus on manifolds. After formulating bilinear stochastic differential equations on general matrix Lie groups, we then consider interest rate models in which the short rate is defined as linear or quadratic functions of the state. Stochastic volatility is also augmented to these models in a way that respects the Riemannian manifold structure of symmetric positive-definite matrices. Methods for numerical integration, parameter identification, pricing, and other practical issues are addressed through examples.

[error in script] [error in script]

Item Type:	Journal Article
Subjects:	H Social Sciences > HB Economic Theory H Social Sciences > HG Finance
Divisions:	Faculty of Social Sciences > Warwick Business School > Finance Group Faculty of Social Sciences > Warwick Business School
Library of Congress Subject Headings (LCSH):	Interest rates -- Mathematical models, Lie groups
Journal or Publication Title:	Quantitative Finance
Publisher:	IOP Publishing
ISSN:	1469-7688
Date:	2011
Volume:	Vol.11
Number:	No.4
Number of Pages:	14
Page Range:	pp. 559-572
Identification Number:	10.1080/14697680903468963
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Sŏul Taehakkyo. [Seoul National University] (SNU), Conference Board of the Mathematical Sciences (CBMS), Han'guk Kwahak Kisul Yŏn'guso [Korea Institute of Science and Technology] (KIST), Center for International Research (U.S.) (CIR), National Research Foundation of Korea (NRF), Association of International Ministries of Korea (AIM), Korea (South). Chisik Kyŏngjebu [Ministry of Knowledge Economy] (MKE)
References:	Bernstein, D.S. and So, W., Some explicit formulas for the matrix exponential. IEEE Trans. Autom. Control, 1993, 38(8), 1228–1232. Bjork, T., A geometric view of interest rate theory. Working Paper Series in Economics and Finance 419, Stockholm School of Economics, 2000. Brennan, M.J. and Schwartz, E.S., Analyzing convertible bonds. J. Financial Quant. Anal., 1980, 15, 907–929. Bridson, M. and Haefliger, A., Metric Spaces of Non-positive Curvature, 1999 (Springer: Berlin). Brigo, D. and Mercurio, F., Interest Rate Models, 2001 (Springer: Berlin). Chirikjian, G., Stochastic models, information, and Lie groups. Preprint, Johns Hopkins University, 2008. Choquet-Bruhat, Y., DeWitt-Morette, C. and Dillard- Bleick, M., Analysis, Manifolds and Physics (Part I), 1982 (North-Holland: Amsterdam). Crouch, P. and Grossman, R., Numerical integration of ordinary differential equations on manifolds. J. Nonlin. Sci., 1993, 3, 1–33. Emery, M., Stochastic Calculus in Manifolds, 1989 (Springer: Berlin). Fletcher, P. and Joshi, S., Principal geodesic analysis on symmetric spaces: statistics of diffusion tensors. Proceedings of ECCV’04 Workshop Computer Vision Approaches to Medical Image Analysis, 2004, 87–98. Flipovic´ , D. and Teichmann, J., On the geometry of the term structure of interest rates. Proc. R. Soc. London A, 2004, 460, 129–167. Hughston, L.P., Stochastic differential geometry, financial modelling, and arbitrage-free pricing. Working Paper, Merrill Lynch, 1994. Iserles, A. and Munthe-Kaas, H., Lie group methods. In Acta Numerica (2000), 2000 (Cambridge University Press: Cambridge). James, J. and Webber, N., Interest Rate Modeling, 2000 (Wiley: Chichester). Kloeden, P.E. and Platen, E., Numerical Solution of Stochastic Differential Equations, 1999 (Springer: Berlin). Lenglet, C., Rousson, M., Deriche, R. and Faugeras, O., Statistics on the manifold of multivariate normal distributions: theory and application to diffusion tensor MRI processing. J. Math. Imag. Vis., 2006, 25(3), 423–444. Munthe-Kaas, H., Higher order Runge–Kutta methods on manifolds. Appl. Numer. Math., 1999, 29, 115–127. Nunes, J. and Webber, N.J., Low dimensional dynamics and the stability of HJM term structure models. Working Paper, University of Warwick, 1997. Sastry, S., Nonlinear Systems, 1999 (Springer: New York). Webber, N., Valuation of financial models with nonlinear state spaces. Preprint, 2000.
URI:	http://wrap.warwick.ac.uk/id/eprint/41582

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item