Group classification of a general bond-option pricing equation of mathematical finance
type: Item
instance of: scholarly article
title: Group classification of a general bond-option pricing equation of mathematical finance
zbMATH Open document ID: 1474.91212
DOI: 10.1155/2014/709871
author: Tanki Motsepa
author: Chaudry Masood Khalique
author: Motlatsi Molati
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 35Q91
zbMATH DE Number: 7022923
Wikidata QID: Q59040802
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/709871
OpenAlex ID: W1980546295
cites work: The pricing of options and corporate liabilities
cites work: Q4905685
cites work: An equilibrium characterization of the term structure
cites work: A theory of the term structure of interest rates
cites work: Pricing Interest-Rate-Derivative Securities
cites work: Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation
cites work: CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
cites work: Lie group classification of the generalized Lane-Emden equation
cites work: Symmetry classification of collapsible tube model incorporating tension
cites work: Group classification of a class of equations arising in financial mathematics
cites work: Lie symmetry analysis of the time-variable coefficient B-BBM equation
cites work: Symmetry classification and invariant solutions of the variable coefficient BBM equation
cites work: Invariance properties of a general bond-pricing equation
cites work: Singular invariant equation for the \((1+1)\) Fokker-Planck equation.
cites work: Complete Invariant Characterization of Scalar Linear (1+1) Parabolic Equations
cites work: New solutions to the bond-pricing equation via Lie's classical method
cites work: Fundamental solutions for zero-coupon bond pricing models
cites work: Zero‐coupon bond prices in the Vasicek and CIR models: Their computation as group‐invariant solutions
cites work: An optimal system and group-invariant solutions of the Cox-Ingersoll-Ross pricing equation
cites work: Invariant approaches to equations of finance
cites work: Complete Specification of Some Partial Differential Equations That Arise in Financial Mathematics
cites work: Lie symmetry analysis of differential equations in finance
cites work: Symmetry reductions, dynamical behavior and exact explicit solutions to the Gordon types of equations
description: scientific article; zbMATH DE number 7022923