Elementary functions solutions to the Bachelier model generated by Lie point symmetries
Evangelos Melas
TL;DR
This paper uses Lie point symmetries to generate new elementary function solutions to the Bachelier model PDE, aiding interest rate option valuation under negative interest rate conditions.
Contribution
It identifies Lie symmetries of the Bachelier PDE and derives new elementary solutions from previous solutions, expanding analytical options for the model.
Findings
Generated new elementary solutions using Lie symmetries
Extended previous solutions to a broader class of functions
Facilitated analytical valuation of interest rate options
Abstract
Under the recent negative interest rate situation, the Bachelier model has been attracting attention and adopted for evaluating the price of interest rate options. In this paper we find the Lie point symmetries of the Bachelier partial differential equation (PDE) and use them in order to generate new classes of denumerably infinite elementary function solutions to the Bachelier model from elementary function solutions to it which we derived in a previous publication.
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Taxonomy
TopicsNonlinear Waves and Solitons · Molecular spectroscopy and chirality · Quantum chaos and dynamical systems