Under MRGP model, the value of [P.sup.[infinity]] (V) is given by
In this section, we use NCIMs for solving the free-boundary PDEs (2)-(6) under four stochastic volatility processes: GBMP, MRGP, MRSRP, and MRLP.
The Matlab command "fminsearch" is used to search the approximate parameters [l.sub.k], k = 1, 2, with initial values [l.sub.k] = 1, k = 1,2, besides we use the technique in  to get the optimal [V.bar] for MRGP and MRLP models since it achieves more accurate results.
Caption: Figure 3: Early exercise boundaries (left) under MRGP model with T/2000 for FDM and L = 6 for NCIM, NCIM errors in log-scale versus L (right).