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Open AccessArticle

Symmetry Analysis of an Interest Rate Derivatives PDE Model in Financial Mathematics

Centre for Computational Finance and Economic Agents, University of Essex, Colchester CO4 3SQ, UK
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Symmetry 2019, 11(8), 1056; https://doi.org/10.3390/sym11081056
Received: 23 July 2019 / Revised: 8 August 2019 / Accepted: 12 August 2019 / Published: 16 August 2019
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Abstract

We perform Lie symmetry analysis to a zero-coupon bond pricing equation whose price evolution is described in terms of a partial differential equation (PDE). As a result, using the computer software package SYM, run in conjunction with Mathematica, a new family of Lie symmetry group and generators of the aforementioned pricing equation are derived. We furthermore compute the exact invariant solutions which constitute the pricing models for the bond by making use of the derived infinitesimal generators and the associated similarity reduction equations. Using known solutions, we again compute more solutions via group point transformations. View Full-Text
Keywords: Lie symmetry analysis; zero-coupon bond; invariant solutions; interest rate derivatives model; partial differential equation Lie symmetry analysis; zero-coupon bond; invariant solutions; interest rate derivatives model; partial differential equation
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Kaibe, B.C.; O’Hara, J.G. Symmetry Analysis of an Interest Rate Derivatives PDE Model in Financial Mathematics. Symmetry 2019, 11, 1056.

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