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Interest rate models on lie groups

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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

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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.

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
Official 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)
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URI: http://wrap.warwick.ac.uk/id/eprint/41582

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