Initial Share price, S 100 Strike price, K 105 Interest rate, r 0.05 Drift of stock price, m 0.1 (Note : drift of stock price is not used, since in a risk neutral world S grows at the risk free rate , µ = r ) Volatility, sigma 0.2 Time to maturity, T 1 Timesteps, dt 0.01 Time Sim 1 Sim 2 Sim 3 Sim 4 Sim 5 Sim 6 Sim 7 Sim 8 Sim 9 Sim 10 0 100 100 100 100 100 100 100 100 100 100 0.01 102.0683 98.24254 98.87855 101.5431 103.5184 95.2749 100.6461 99.78637 99.00934 100.2764 0.02 101.4991 98.61617 97.02375 101.1719 102.4285 94.31592 104.9234 97.97129 97.66684 100.5254 0.03 103.9092 95.88536 98.73509 101.2475 100.6396 95.65295 105.1794 96.87865 100.1202 102.8404 0.04 105.4658 96.49318 95.99575 100.8647 100.0629 95.61603 105.1857 97.00646 102.7422 101.5916 0.05 104.0441 95.42383 97.11991 100.2396 103.8199 94.83106 106.3178 94.93666 101.4046 101.7524 0.06 102.8777 94.85561 94.98678 99.12134 103.6873 95.19411 108.5881 96.54616 104.2306 102.7966 0.07 104.8219 96.31778 97.91917 103.7426 105.3917 98.65604 108.5898 96.9319 104.8551 102.811 0.08 102.2478 93.70715 99.15029 102.524 103.6953 97.75714 105.6874 92.55381 104.2869 101.702 0.09 101.0226 94.90227 99.09491 103.7004 104.5613 97.88188 110.0557 92.73299 105.5291 101.0615 0.1 102.3281 94.85395 99.37359 109.5999 101.7666 98.89262 106.757 92.61333 103.6116 101.3234 0.11 101.9881 93.47635 101.1619 106.6899 98.91664 98.47037 103.2891 91.87067 105.3945 105.7324 0.12 104.5612 92.52656 99.98202 102.853 100.3959 98.39895 100.5109 87.9918 103.6261 101.2889 0.13 106.766 91.557 99.69919 103.75 100.365 100.9838 101.5454 89.87482 102.654 102.1388 0.14 106.357 92.56212 99.62914 101.9401 100.8362 97.88202 103.1083 90.63206 99.44344 100.4932 0.15 109.1374 90.42656 98.88038 99.54012 101.9623 96.92416 103.3545 90.19795 98.62913 100.4467 … … … … … … … … … … … 0.95 132.726 115.302 121.9 93.21048 74.42675 104.8382 137.0511 83.4953 78.38809 106.5505 0.96 132.0004 115.3534 121.933 95.04815 75.91156 106.4852 138.3202 81.60178 77.16147 104.5654 0.97 133.2309 113.4452 125.1421 99.45439 74.88303 108.0976 138.6531 81.6501 77.80683 107.2737 0.98 131.967 110.7992 122.8945 98.97497 74.8229 106.5214 135.3777 84.09324 77.13906 108.8608 0.99 132.0259 112.8501 120.0849 97.57811 75.52392 106.7636 137.2358 84.23462 77.61826 109.955 1 130.4202 115.9259 122.0662 97.48344 75.87743 105.2443 135.0986 85.72814 78.28576 108.3915 Call Payoff : Max[S(T)-K, 0] Call Payoff for each "run" 25.42017 10.92586 17.06618 0 0 0.24429 30.09859 0 0 3.391519 Mean payoff 8.71466 PV of "mean payoff" 8.289641 equals the MCS call pemium Put Payoff : Max[K-S(T), 0] Put Payoff for each "run" 0 0 0 7.516557 29.12257 0 0 19.27186 26.71424 0 Mean payoff 8.262523 PV of "mean payoff" 7.859555 equals the MCS put pemium Table 17.4 : Monte Carlo Simulation to Value a Call and a Put Option