PRICING AND HEDGING BARRIER OPTIONS IN A HYPER-EXPONENTIAL ADDITIVE MODEL

Marc Jeannin () and Martijn Pistorius ()
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Marc Jeannin: Models and Methodology Group, Risk Management Department, Nomura International plc, Nomura House 1 St Martin's-le-Grand, London EC1A 4NP, UK
Martijn Pistorius: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 05, 657-681

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: Hyper-exponential additive processes; matrix Wiener-Hopf factorization; first passage times; barrier options; multi-dimensional Laplace transform; Fourier transform; sensitivities (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219024910005954

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