Functional quantization for numerics with an application to option pricing

TitleFunctional quantization for numerics with an application to option pricing
Publication TypeJournal Article
Year of Publication2005
AuthorsGilles Pagès, and Jacques Printems
JournalMonte Carlo Methods and Appl.
KeywordsAsian option, Brownian motion, functional quantization, Heston model, Karhunen-Loève expansion, product quantizers, Romberg extrapolation, SDE, stochastic volatility

We investigate in this paper the numerical performances of quadratic functional quantization with some applications to Finance. We emphasize the rôle played by the so-called product quantizers and the Karhunen-Loève expansion of Gaussian processes, in particular the Brownian motion. We show how to build some efficient functional quantizers for Brownian diffusions. We propose a quadrature formula based on a Romberg log-extrapolation of “crude” functional quantization which speeds up significantly the method. Numerical experiments are carried out on two European option pricing problems: vanilla and Asian Call options in a Heston stochastic volatility model. It suggests that functional quantization is a very efficient integration method for various path-dependent functionals of a diffusion processes: it produces deterministic results which outperforms Monte Carlo simulation for usual accuracy levels.

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