Abstract
We consider a bond‐pricing model described in terms of partial differential equations (PDEs). Classical Lie point symmetry analysis of the considered PDEs resulted in a number of point symmetries being admitted. The one‐dimensional optimal system of subalgebras is constructed. Following the symmetry reductions, we determine the group‐invariant solutions.
Highlights
Over the last few decades, there has been a great interest in the modelling and analysis of problems arising in finance markets
Some of these problems are modelled in terms of partial differential equations (PDEs)
A number of studies have been devoted to the use of symmetry techniques for PDEs arising in the field of finance mathematics
Summary
Over the last few decades, there has been a great interest in the modelling and analysis of problems arising in finance markets. Pooe et al [12], assumed that the spot rate follows the stochastic process (see [4, 5]) given by dx(t) = a(x, t) dt + w(x, t) dZ(t), and ended up solving the model ut w2 uxx (a λ(x, t)w)ux xu. The aim of this paper is to analyze a bond-pricing model and to determine its closed-form solutions using Lie point symmetry techniques. In the present work we assume that the risk free spot rate follows the Itô’s process or stochastic process of the form dx(t) = b(x(t), t)w2(x(t), t) dt + w(x(t), t) dZ(t), with specified drift term b(x(t), t) and the volatility w(x(t), t). The symmetry reductions and construction of groupinvariant solutions are provided in Section 4 and lastly the concluding remarks are given
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