Convergence of Price and Sensitivities in Carr's Randomization Approximation Globally and Near Barrier

Abstract

Barrier options under wide classes of Lévy processes with exponentially decaying jump densities, including the variance gamma model, KoBoL and CGMY models, normal inverse Gaussian processes, and $\beta$-class, are studied. The leading term of asymptotics of the option price and the leading term of asymptotics in Carr's randomization approximation to the price are calculated as the price of the underlying approaches the barrier. We prove that the order of asymptotics is the same in both cases and that the asymptotic coefficient in the asymptotic formula for Carr's randomization approximation converges to the asymptotic coefficient for the price as the number of time steps $N\to+\infty$. Also, we justify Richardson extrapolation of arbitrary order. Similar results are derived for sensitivities and the leading terms of their asymptotics in Carr's randomization approximation. The convergence of prices and sensitivities is proved in appropriate weighted Hölder spaces.

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 — 20 citations exist upstream.

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