Efficient Pricing Options with Barrier and Lookback Features Under Levy Processes

29 Pages Posted: 5 Jun 2011

See all articles by Oleg E. Kudryavtsev

Oleg E. Kudryavtsev

Russian Customs Academy Rostov Branch - Department of Informatics

Sergei Levendorskii

Calico Science Consulting

Date Written: June 4, 2011

Abstract

We derive a general formula for pricing options with barrier and/or lookback features, which covers several types of options studied in the literature and new types of options, and demonstrate that the pricing formula can be efficiently realized using the methodology developed in Kudryavtsev and Levendorskii (Finance Stoch.13: 531-562, 2009). As one of examples, we consider a new type of barrier-lookback options, which expire if the barrier is reached or crossed before maturity, and pay the same amount as standard lookback options otherwise. We demonstrate advantages of our approach in terms of accuracy and convergence.

Keywords: Levy processes, KoBoL, CGMY, barrier options, lookback options, barrier-lookback options, Wiener-Hopf factorization, inverse Laplace transform, Fast Fourier transform

JEL Classification: D81, C61, G31

Suggested Citation

Kudryavtsev, Oleg E. and Levendorskii, Sergei Z., Efficient Pricing Options with Barrier and Lookback Features Under Levy Processes (June 4, 2011). Available at SSRN: https://ssrn.com/abstract=1857943 or http://dx.doi.org/10.2139/ssrn.1857943

Oleg E. Kudryavtsev (Contact Author)

Russian Customs Academy Rostov Branch - Department of Informatics ( email )

Budennovskiy 20
Rostov-on-Don, 344011
Russia

Sergei Z. Levendorskii

Calico Science Consulting ( email )

Austin, TX
United States

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