Martingale property for the Scott correlated stochastic volatility model

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.