PRICES AND SENSITIVITIES OF BARRIER AND FIRST-TOUCH DIGITAL OPTIONS IN LÉVY-DRIVEN MODELS

Mitya Boyarchenko () and Sergei Levendorskiĭ ()
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Mitya Boyarchenko: Department of Mathematics, University of Michigan, 530 Church Street, 2704 East Hall, Ann Arbor, MI 48109-1043, USA
Sergei Levendorskiĭ: Department of Mathematics, The University of Leicester, University Road, Leicester LE1 7RH, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2009, vol. 12, issue 08, 1125-1170

Abstract: We present a fast and accurate FFT-based method of computing the prices and sensitivities of barrier options and first-touch digital options on stocks whose log-price follows a Lévy process. The numerical results obtained via our approach are demonstrated to be in good agreement with the results obtained using other (sometimes fundamentally different) approaches that exist in the literature. However, our method is computationally much faster (often, dozens of times faster). Moreover, our technique has the advantage that its application does not entail a detailed analysis of the underlying Lévy process: one only needs an explicit analytic formula for the characteristic exponent of the process. Thus our algorithm is very easy to implement in practice. Finally, our method yields accurate results for a wide range of values of the spot price, including those that are very close to the barrier, regardless of whether the maturity period of the option is long or short.

Keywords: Option pricing; greeks; barrier options; first-touch digitals; Lévy processes; Fast Fourier transform; Carr's randomization; KoBoL processes; CGMY model; Normal Inverse Gaussian processes; Variance Gamma processes; Wiener–Hopf factorization (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (14)

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DOI: 10.1142/S0219024909005610

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