Martingale property for the Scott correlated stochastic volatility model

TL;DR

This paper investigates the martingale property of a Scott correlated stochastic volatility model, establishing conditions under which the asset price process is a true martingale based on the correlation coefficient.

Contribution

It provides a rigorous analysis of the martingale property in the model for arbitrary correlation, extending previous results with necessary and sufficient conditions.

Findings

The asset price process is a true martingale if and only if the correlation coefficient  in [-1,0].

The process is uniformly integrable under the same correlation conditions.

The study applies Bernard et al.'s criteria to the Scott model with arbitrary correlation.

Abstract

In this paper, we study the martingale property for a Scott correlated stochastic volatility model, when the correlation coefficient between the Brownian motion driving the volatility and the one driving the asset price process is arbitrary. For this study we verify the martingale property by using the necessary and sufficient conditions given by Bernard \emph{et al.} \cite{Bernard}. Our main results are to prove that the price process is a true and uniformly integrable martingale if and only if $\rho \in [-1,0]$ for two transformations of Brownian motion describing the dynamics of the underling asset.