  Recursive Marginal Quantization (RMQ) allows fast approximation of solutions
to stochastic differential equations in one-dimension. When applied to two
factor models, RMQ is inefficient due to the fact that the optimization problem
is usually performed using stochastic methods, e.g., Lloyd's algorithm or
Competitive Learning Vector Quantization. In this paper, a new algorithm is
proposed that allows RMQ to be applied to two-factor stochastic volatility
models, which retains the efficiency of gradient-descent techniques. By
margining over potential realizations of the volatility process, a significant
decrease in computational effort is achieved when compared to current
quantization methods. Additionally, techniques for modelling the correct
zero-boundary behaviour are used to allow the new algorithm to be applied to
cases where the previous methods would fail. The proposed technique is
illustrated for European options on the Heston and Stein-Stein models, while a
more thorough application is considered in the case of the popular SABR model,
where various exotic options are also priced.
