Interest rate models and Whittaker functions

TL;DR

This paper explores interest rate models that utilize Whittaker functions, providing closed-form solutions for zero-coupon bond values through advanced mathematical techniques like Laplace transforms and hypergeometric functions.

Contribution

It introduces a unified analytical approach for several interest rate models using Whittaker functions, offering explicit solutions for bond valuation.

Findings

Closed-form solutions for zero-coupon bonds in various models

Application of Laplace transform and hypergeometric functions

Unified structure of interest rate models via Whittaker functions

Abstract

I present the technique which can analyse some interest rate models: Constantinides-Ingersoll, CIR-model, geometric CIR and Geometric Brownian Motion. All these models have the unified structure of Whittaker function. The main focus of this text is closed-form solutions of the zero-coupon bond value in these models. In text I emphasize the specific details of mathematical methods of their determination such as Laplace transform and hypergeometric functions.