Lie Symmetry On Bond-option Formula For Vasicek Model

Derivation of Bond-Option formula is of great importance hence shown.Bond-Optiont pricing partial differential equation admits Lie group classi-fication[4]and some arbitrary parameters can allow this equation to admit some symmetry Lie algebra.Some of the constants that produced from the classification allow some globally known models in Financial Mathe-matics and Financial Engineering such as Black-Scholes equation,Vasicek and Cox-Ingersol-Ross.This paper will give Lie symmetry for Vasicek model but even for Black-Schole model and surly CIR can be find on a very important generalized form of Bond-Option PDE.And will end with solution for Vasicek,for this general form Bond-Option PDE the Vacisek model as per papers has not yet been discussed which brings to my at-tension to focus on its solution.