Wavelet Galerkin pricing of American options on Lévy driven assets

Abstract

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.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 109 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.