  Recursive marginal quantization (RMQ) allows the construction of optimal
discrete grids for approximating solutions to stochastic differential equations
in d-dimensions. Product Markovian quantization (PMQ) reduces this problem to d
one-dimensional quantization problems by recursively constructing product
quantizers, as opposed to a truly optimal quantizer. However, the standard
Newton-Raphson method used in the PMQ algorithm suffers from numerical
instabilities, inhibiting widespread adoption, especially for use in
calibration. By directly specifying the random variable to be quantized at each
time step, we show that PMQ, and RMQ in one dimension, can be expressed as
standard vector quantization. This reformulation allows the application of the
accelerated Lloyd's algorithm in an adaptive and robust procedure. Furthermore,
in the case of stochastic volatility models, we extend the PMQ algorithm by
using higher-order updates for the volatility or variance process. We
illustrate the technique for European options, using the Heston model, and more
exotic products, using the SABR model.
