Pricing the zero-coupon bond of the extended Cox-Ingersoll-Ross model using Malliavin calculus

TL;DR

This paper introduces a Malliavin calculus-based Dyson series formula for efficiently pricing zero-coupon bonds in the extended Cox-Ingersoll-Ross model, offering a novel approach that bypasses the need for forward rate data.

Contribution

It develops a new fast-converging series formula for bond pricing in the extended CIR model using Malliavin calculus, providing an alternative to traditional methods.

Findings

The series formula converges rapidly for practical computation.

The method depends only on drift and volatility, not on forward rates.

It offers a new solution to Riccati equations with time-dependent coefficients.

Abstract

In this paper, we price the zero-coupon bond of the extended Cox-Ingersoll-Ross model by a Dyson type formula established in one of the authors' paper Jin, Peng and Schelllhorn (2016) using Malliavin calculus. This formula provides a fast convergent series to represent the bond price, and it depends on the given drift and volatility of the interest rate process but not the instantaneous forward rate used in Maghsoodi (1996). This expression can be also regarded as a new solution to a class of Reccati equations with time-dependent coefficients.