# Fast Quantization of Stochastic Volatility Models

## TL;DR

This paper introduces a new efficient algorithm for applying recursive marginal quantization to two-factor stochastic volatility models, significantly reducing computational effort and handling boundary conditions effectively.

## Contribution

A novel gradient-descent based algorithm enabling fast quantization of two-factor stochastic volatility models, overcoming previous inefficiencies and boundary issues.

## Key findings

- Efficient quantization of Heston and Stein-Stein models for European options.
- Successful application to SABR model with exotic options.
- Significant reduction in computational time compared to existing methods.

## Abstract

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.