Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

الملخص EN

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.