PRICING OF FIRST TOUCH DIGITALS UNDER NORMAL INVERSE GAUSSIAN PROCESSES

Oleg Kudryavtsev () and Sergei Levendorskiǐ ()
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Oleg Kudryavtsev: Department of Informatics, Russian Customs Academy Rostov Branch, Budennovskiy 20, Rostov-on-Don, 344011, Russia
Sergei Levendorskiǐ: Department of Economics, University of Texas at Austin, 1 University Station C3100, Austin, TX 78712, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 06, 915-949

Abstract: We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Brownian model and double exponential jump-diffusion model. Numerical results are produced to show that for typical parameters values, the relative error of the Brownian motion approximation to NIG price can be 2–3 dozen percent if the spot price is at the distance 0.05–0.2 from the barrier (normalized to one). A similar effect is observed for approximations by the double exponential jump-diffusion model, if the jump component of the approximation is significant. We show that two jump-diffusion processes can give approximately the same results for European options but essentially different results for first touch digitals and barrier options. A fast approximate pricing formula under NIG is derived.

Keywords: First touch digitals; Normal Inverse Gaussian processes; jump-diffusions; Lévy processes; fast pricing (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024906003834

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