@article {FunctionalQuantizationNum,
	title = {Functional quantization for numerics with an application to option pricing},
	journal = {Monte Carlo Methods and Appl.},
	volume = {11},
	number = {11},
	year = {2005},
	pages = {407-446},
	abstract = {    We investigate in this paper the numerical performances of quadratic functional quantization with some applications to Finance. We emphasize the r{\^o}le played by the so-called product quantizers and the Karhunen-Lo{\`e}ve 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 {\textquotedblleft}crude{\textquotedblright} 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. },
	keywords = {Asian option, Brownian motion, functional quantization, Heston model, Karhunen-Lo{\`e}ve expansion, product quantizers, Romberg extrapolation, SDE, stochastic volatility},
	attachments = {http://quantize.maths-fi.com/sites/default/files/Functional Quantization Num.pdf},
	author = {Gilles Pag{\`e}s and Jacques Printems}
}
