Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representation

TL;DR

This paper introduces a new analytical method using Neumann series of Bessel functions for pricing double barrier options on homogeneous diffusions, applicable even without known transition densities, and demonstrates its effectiveness through an extended jump to default model.

Contribution

It presents a novel, analytically tractable Bessel function series representation for pricing double barrier options on general diffusions, including cases with unknown transition densities.

Findings

Method is efficient and easy to implement.

Applicable to a wide class of diffusions.

Successfully models empirical regularities with an extended jump to default model.

Abstract

This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional time-homogeneous diffusions even for the cases where the corresponding transition density is not known. The proposed numerical method is shown to be efficient and simple to implement. To illustrate the flexibility and computational power of the algorithm, we develop an extended jump to default model that is able to capture several empirical regularities commonly observed in the literature.