The large-maturity smile for the Stein-Stein model

We compute the large-maturity smile for the correlated Stein-Stein stochastic volatility model dSt=StYtdWt1,dYt=κ(θ−Yt)dt+σdWt2, dWt1dWt2=ρdt, using the known closed-form solution for the characteristic function of the log stock price given in Schöbel and Zhu (1999). The Stein-Stein model is not covered by the results in Forde and Kumar (submitted for publication) and Jacquier et al. (2013) because the volatility fails to satisfy the sublinear growth condition in Forde and Kumar (submitted for publication) and is not an affine model.1