Fundamental solution of bond pricing in the Ho-Lee stochastic interest rate model under the invariant criteria

Abstract

We study the fundamental solution of bond-pricing in the Ho-Lee stochastic interest rate model under the invariant criteria. We obtain transformations between Ho-Lee model with the corresponding linear (1+1) partial differential equation and the first Lie canonical form which is identical to the classical heat equation. These transformations help us to generate the fundamental solution for the Ho-Lee model with respect to the fundamental solution of the classical heat equation sense. Moreover, as a financial application of the Ho-Lee model, we choose the drift term from power functions and perform simulations via Milstein method. Furthermore, we obtain important results for the parameter calibration of the corresponding drift term by using the simulation results.

Keywords

• Ho-Lee stochastic interest rate model,heat equation,canonical Lie forms,Lie symmetry analysis,invariant criteria

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