Pricing and hedging barrier options in a hyper-exponential additive model
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.
Keywords
Cite
@article{arxiv.0812.3117,
title = {Pricing and hedging barrier options in a hyper-exponential additive model},
author = {Marc Jeannin and Martijn Pistorius},
journal= {arXiv preprint arXiv:0812.3117},
year = {2009}
}
Comments
26 pages, 8 figures. To appear in IJTAF