Before revision:  To show how our symmetrization scheme works, we will present some numerical results applying (path-independent) Euler-Maruyama approximation to our scheme, comparing them with the path-dependent Euler-Maruyama scheme when the underlying process follows Black-Scholes and some CEVmodels .
After revision:  To show how our symmetrization scheme works, we will present some numerical results applying (path-independent) Euler-Maruyama approximation to our scheme, comparing them with the path-dependent Euler-Maruyama scheme when the underlying process follows Black-Scholes , CEV, Heston, and (\lambda) -SABR, respectively .