Functional quantization for pricing derivatives
Pages, Gilles ; Printems, Jacques
HAL, hal-00003092 / Harvested from HAL
We investigate in this paper the numerical performances of quadratic functional quantization and their applications to Finance. We emphasize the rôle played by the so-called product quantizers and the Karhunen-Loève expansion of Gaussian processes. Numerical experiments are carried out on two classical pricing problems: Asian options in a Black-Scholes model and vanilla options in a stochastic volatility Heston model. Pricing based on "crude" functional quantization is very fast and produce accurate deterministic results. When combined with a Romberg $\log$-extrapolation, it always outperforms Monte Carlo simulation for usual accuracy levels.
Publié le : 2004-10-18
Classification:  SDE,  Asian option,  stochastic volatility,  Heston model,  Romberg extrapolation,  Brownian motion,  Karhunen-Loève expansion,  Functional quantization,  Product quantizers,  60E99, 60H10,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00003092,
     author = {Pages, Gilles and Printems, Jacques},
     title = {Functional quantization for pricing derivatives},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00003092}
}
Pages, Gilles; Printems, Jacques. Functional quantization for pricing derivatives. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003092/