Lie Symmetry Algebra of the Longstaff-Schwartz Pricing Equation
The determination, by Lie's point-symmetry method, of the symmetry group of the linear second-order parabolic PDE (a Kolmogorov backward equation) arising from the two-factor Longstaff-Schwartz interest-rate model. Students learn how case analysis on the equation's four drift constants yields the largest and smallest admissible symmetry algebras, and how those symmetry algebras are classified by their Lie-algebra structure up to isomorphism.
2501.00155
The Longstaff-Schwartz model is a two-factor, Cox-Ingersoll-Ross-type model of the short-term interest rate used to price American-style options. Through the Ito formula its associated pricing functi…