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

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