Pricing and hedging barrier options in a hyper-exponential additive model

TL;DR

This paper presents a semi-analytical algorithm for pricing and hedging barrier options within a hyper-exponential additive model, offering explicit formulas for prices and Greeks, validated through numerical examples and Monte Carlo comparisons.

Contribution

It introduces a novel explicit semi-analytical method using matrix Wiener-Hopf factorization for barrier option pricing in a hyper-exponential additive framework.

Findings

Method is fast, accurate, and stable.

Provides explicit formulas for prices and Greeks.

Validated against Monte Carlo simulations.

Abstract

In this paper we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage probability. The solution rests on a randomization and an explicit matrix Wiener-Hopf factorization. Employing this result we derive explicit expressions for the Laplace-Fourier transforms of the prices and Greeks of barrier options. As a numerical illustration, the prices and Greeks of down-and-in digital and down-and-in call options are calculated for a set of parameters obtained by a simultaneous calibration to Stoxx50E call options across strikes and four different maturities. By comparing the results with Monte-Carlo simulations, we show that the method is fast, accurate, and stable.