In this paper we develop an algorithm to calculate  prices and Greeks of barrier options driven by a class of additive processes. Additive processes are time-inhomogeneous Levy processes, or equivalently, processes with independent but inhomogeneous increments . We obtain an explicit semi-analytical expression for the first-passage probability of an additive process with hyper-exponential jumps . 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 prices and Greeks of digital and barrier options. As  numerical illustration, the model is simultaneously calibrated to Stoxx50E call options at four different maturities and subsequently prices and Greeks of down-and-in digital and down-and-in call options are calculated . Comparison with Monte Carlo simulation results shows that the method is fast, accurate, and stable.
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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the
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driven by a class of additive processes. Additive processes are time-inhomogeneous Levy processes, or equivalently, processes with independent but inhomogeneous increments
in a hyper-exponential additive model with piecewise constant parameters
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of an additive process with hyper-exponential jumps
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Wiener- Hopf
Wiener-Hopf
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Laplace(-Fourier) transforms of
Laplace-Fourier transforms of the
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digital and
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model is simultaneously calibrated to Stoxx50E call options at four different maturities and subsequently
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. Comparison with Monte Carlo simulation results shows
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