16.20 Consider the Scott (1987), and the later Chesney and Scott (1989) model which introduced for the first time in finance a so-called mean-reverting volatility process. The model is dSt = μSStdt + eYtStdWt, dYt = α(Y¯ − Yt)dt + σY dZt with the difference between the two papers being that in the first paper the two Brownian motions are uncorrelated (ρ = 0).

Calculate the dynamics of the volatility term eY t and its mean and variance. Use Milstein scheme and generate and plot 10 paths.