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Zbl 1134.91450
Matache, Ana-Maria; Nitsche, Pál-Andrej; Schwab, Christoph
Wavelet Galerkin pricing of American options on Lévy driven assets. (English)
[J] Quant. Finance 5, No. 4, 403-424 (2005). ISSN 1469-7688; ISSN 1469-7696/e

Summary: The price of an American-style contract on assets driven by a class of Markov processes containing, in particular, Lévy processes of pure jump type with infinite jump activity is expressed as the solution of a parabolic variational integro-differential inequality (PIDI). A Galerkin discretization in logarithmic price using a wavelet basis is presented. Log-linear complexity in each time-step is achieved by wavelet compression of the moment matrix of the price process' jump measure and by wavelet preconditioning of the large matrix LCPs at each time-step. Efficiency is demonstrated by numerical experiments for pricing American put contracts on various jump-diffusion and pure jump models. Failure of the smooth pasting principle is observed for American put contracts for certain finite variation pure jump price processes.

MSC 2000:: *91B28 Finance etc.

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