Quantization and its numerical applications

[Bastian Gross]

Hello Quantneties,

I want to ask, is someone interested in functional quantization?
And not only because of an word joke with QUANTization und QUANTnet. :-\"


Functional quantization is an very useful alternative solution for pricing options, especially pathdepent options, in contrast to Monte Carlo methods.

I know, that (dutch) ABN Amro use a software packet to pricing its Option by functional quantization.
Do anyone of you know much more about this mathematical method in financial engineering?



The Book of Graf and Luschgy:
Foundations of Quantization for Probability Distributions (http://www.amazon.com/Foundations-Quantization-Probability-Distributions-Mathematics/dp/3540673946/ref=sr_1_1?ie=UTF8&s=books&qid=1199374969&sr=8-1)

http://ecx.images-amazon.com/images/I/41AP07FPR2L._BO2,204,203,200_PIsitb-dp-500-arrow,TopRight,45,-64_OU03_AA240_SH20_.jpg (http://www.amazon.com/Foundations-Quantization-Probability-Distributions-Mathematics/dp/3540673946/ref=sr_1_1?ie=UTF8&s=books&qid=1199374969&sr=8-1)

And here are two articels about Quantization and its numerical applications to pricing option:

path-depent European options (Quadratic optimal functional quantization of stochastic processes and numerical applications (http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.4450v1.pdf))
Swing Options (Optimal quantization for the pricing of swing options (http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.2110v1.pdf))
I'm prepared to answer further questions.

[Andy]

Looks like good book for EE and Math people. Lot of equations ;)
I like to know how functional quantization is used in finance. Or at least some piece of code so I can compare with the old Black Scholes, Finite Different option pricing we all learn.

[Vic_Siqiao]

is it sort of optimization? lots of probability spaces and other math stuff.

[Yuriy]

I see that part of it is computational geometry, but don't know about the rest.

[Bastian Gross]

Okay, I see there are some question about FQ (= functional quantization).

At Monte Carlo methods you use some randomnumbers generated by pseudo-random number generator (PRNG) (like Mersenne-Twister or linear congruential generator (LCG)) to calculate expectation value. But problems with deterministic pseudo-random number generators avoid good performance, so efficient MC-methods range between 10.000 and 100.000 simulations.
To speed-up performance one uses variance reduction.

By calculation expectation value with FQ you must estimate some optimal codebooks (this is the "computational geometry :smt104and probability spaces stuff" :smt045) and uses these to compute for instance derivate-prices.

I rememer you calculation expectation value is the main subject of pricings derivates.