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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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Official URL: http://dx.doi.org/10.1080/14697680903468963

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

Dates:

Date	Event
2011	Published

Volume:

Vol.11

Number:

No.4

Number of Pages:

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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