The m-th order moment of the log-price variable in the Stein-Stein model

 

Insert risk free interest rate r(-1 < r < 1)
Insert correlation coefficient r (-1 < r < 1)
Insert vol of vol e (years-1/2) (0 ≤ e ≤ 1)
Insert long term mean q (years-1/2) (q≥ 0)
Insert speed of mean reversion c (years-1/2) (c≥ 0)
Insert initial stochastic volatility (years-1/2) (0 < ≤1)
Insert initial value of the log-price variable (0 < ≤ 1)    
Insert time t' (years) (0 < t' < 2.0)
Insert moment order m (0 < m ≤ 2)
Insert Monte Carlo sample size N (0 < N ≤ 100000)
Theoretical m-th order moment of the log-price xt' (explicit formula)
Numerical m-th order moment of the log-price xt' (Monte Carlo method)