Enhanced group analysis of a semi-linear general bond-pricing equation

TL;DR

This paper performs an advanced group classification of a semi-linear bond-pricing equation, identifying symmetries that lead to invariant solutions relevant for financial options under specific conditions.

Contribution

It introduces an enhanced classification method using equivalence transformations, revealing subclasses with larger symmetry algebras for solving bond-pricing equations.

Findings

Identification of subclasses with larger Lie algebras

Derivation of non-trivial invariant solutions

Application to terminal and barrier option conditions

Abstract

The enhanced group classification of a semi-linear generalization of a general bond-pricing equation is carried out by employing the underlying equivalence and additional equivalence transformations. The knowledge of the sub classes with larger Lie algebras than the general case enable us to find non trivial invariant solutions under the terminal and the barrier option condition.