Explicit solution simulation method for the 3/2 model

TL;DR

This paper derives an explicit weak solution for the 3/2 stochastic volatility model, enabling a new simulation algorithm for option pricing that performs comparably to existing methods.

Contribution

It introduces an explicit weak solution for the non-affine 3/2 model, facilitating an efficient simulation algorithm for option pricing.

Findings

Simulation algorithm performs comparably to existing methods.

Explicit solution improves computational efficiency.

Numerical tests validate the approach.

Abstract

An explicit weak solution for the 3/2 stochastic volatility model is obtained and used to develop a simulation algorithm for option pricing purposes. The 3/2 model is a non-affine stochastic volatility model whose variance process is the inverse of a CIR process. This property is exploited here to obtain an explicit weak solution, similarly to Kouritzin (2018). A simulation algorithm based on this solution is proposed and tested via numerical examples. The performance of the resulting pricing algorithm is comparable to that of other popular simulation algorithms.