Robust product Markovian quantization

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