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arXiv · 0812.3117

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

Marc Jeannin·Martijn Pistorius
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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.

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Marc Jeannin, Martijn Pistorius. 2009-12-31. Pricing and hedging barrier options in a hyper-exponential additive model. https://arxiv.org/abs/0812.3117

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