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Standard Monte Carlo Simulation Of A Standard Brownian Motion 0.0 RAND() Uniform Random Variable Between 0 and 1 0.0 NORMSINV(Rand()) Normal Random Variable with Mean 0 StDev 1 NORMSINV(X) Function...

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Standard
    Monte Carlo Simulation Of A Standard Brownian Motion                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                0.0
        RAND()        Uniform Random Variable Between 0 and 1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    0.0
        NORMSINV(Rand())        Normal Random Variable with Mean 0 StDev 1
        NORMSINV(X)        Function Transforming X on [0, 1] to Y on [-Infinity, +Infinity]
                so that uniform density of X is transformed to Normal with Mean 0 StDev 1
                This function is the same as inverse function to Cumulative density N(X)
                                        0.00    0.01    0.02    0.03    0.04    0.05    0.06    0.07    0.08    0.09    0.10    0.11    0.12    0.13    0.14    0.15    0.16    0.17    0.18    0.19    0.20    0.21    0.22    0.23    0.24    0.25    0.26    0.27    0.28    0.29    0.30    0.31    0.32    0.33    0.34    0.35    0.36    0.37    0.38    0.39    0.40    0.41    0.42    0.43    0.44    0.45    0.46    0.47    0.48    0.49    0.50    0.51    0.52    0.53    0.54    0.55    0.56    0.57    0.58    0.59    0.60    0.61    0.62    0.63    0.64    0.65    0.66    0.67    0.68    0.69    0.70    0.71    0.72    0.73    0.74    0.75    0.76    0.77    0.78    0.79    0.80    0.81    0.82    0.83    0.84    0.85    0.86    0.87    0.88    0.89    0.90    0.91    0.92    0.93    0.94    0.95    0.96    0.97    0.98    0.99    1.00
    X(n)=X(n-1)+E(n)*Sqrt(delta_t)                                    t0    t1    t2    t3    t4    t5    t6    t7    t8    t9    t10    t11    t12    t13    t14    t15    t16    t17    t18    t19    t20    t21    t22    t23    t24    t25    t26    t27    t28    t29    t30    t31    t32    t33    t34    t35    t36    t37    t38    t39    t40    t41    t42    t43    t44    t45    t46    t47    t48    t49    t50    t51    t52    t53    t54    t55    t56    t57    t58    t59    t60    t61    t62    t63    t64    t65    t66    t67    t68    t69    t70    t71    t72    t73    t74    t75    t76    t77    t78    t79    t80    t81    t82    t83    t84    t85    t86    t87    t88    t89    t90    t91    t92    t93    t94    t95    t96    t97    t98    t99    t100
    delta_t    Sqrt(delta_t)    Xo=                    Traj    1    0.0    0.1    0.4    0.5    0.3    0.2    0.3    0.1    0.1    0.1    0.1    0.2    0.1    -0.0    -0.1    -0.1    0.0    -0.0    -0.0    0.0    -0.1    -0.0    -0.0    -0.2    -0.5    -0.4    -0.4    -0.2    -0.3    -0.3    -0.4    -0.4    -0.3    -0.1    -0.2    -0.3    -0.2    -0.1    0.0    -0.0    -0.2    -0.0    -0.0    -0.3    -0.2    -0.4    -0.4    -0.4    -0.5    -0.5    -0.6    -0.6    -0.6    -0.6    -0.7    -0.7    -0.6    -0.7    -0.7    -0.9    -0.9    -0.8    -0.9    -0.8    -0.7    -0.6    -0.5    -0.7    -0.8    -1.0    -1.0    -0.9    -1.1    -1.1    -1.2    -1.2    -1.2    -1.2    -1.1    -1.2    -1.4    -1.4    -1.5    -1.6    -1.7    -1.5    -1.4    -1.4    -1.4    -1.5    -1.5    -1.4    -1.4    -1.4    -1.6    -1.6    -1.7    -1.5    -1.5    -1.5    -1.6
    0.01    0.1    0                    Traj    2    0.0    -0.1    0.1    0.1    0.1    0.0    -0.0    0.0    0.2    0.2    0.2    0.1    0.2    0.2    0.5    0.5    0.5    0.5    0.7    0.5    0.4    0.6    0.4    0.4    0.4    0.4    0.5    0.2    0.2    0.3    0.2    0.3    0.3    0.3    0.3    0.3    0.3    0.2    0.1    0.2    0.1    -0.0    -0.1    0.1    0.1    0.2    0.2    0.3    0.4    0.4    0.4    0.4    0.5    0.5    0.5    0.4    0.3    0.2    0.1    0.3    0.3    0.3    0.3    0.3    0.3    0.4    0.3    0.4    0.3    0.4    0.4    0.5    0.5    0.7    0.7    0.6    0.6    0.6    0.6    0.7    0.6    0.6    0.6    0.8    0.8    0.8    0.9    0.7    0.7    0.7    0.6    0.7    0.7    0.8    0.8    0.8    0.7    0.6    0.7    0.6    0.6
                                Traj    3    0.0    -0.2    -0.4    -0.4    -0.5    -0.3    -0.3    -0.3    -0.2    -0.3    -0.4    -0.4    -0.4    -0.3    -0.4    -0.4    -0.3    -0.1    -0.0    -0.1    -0.1    0.1    0.1    -0.0    -0.0    -0.0    -0.2    -0.1    -0.1    0.0    -0.0    -0.1    -0.2    -0.2    -0.2    -0.2    -0.2    -0.2    -0.1    -0.1    0.1    0.2    0.3    0.2    0.4    0.2    0.3    0.3    0.3    0.1    0.1    0.0    0.0    0.1    0.0    0.0    -0.1    -0.2    -0.3    -0.3    -0.6    -0.5    -0.6    -0.8    -0.8    -1.0    -0.9    -0.8    -0.7    -0.7    -0.8    -0.8    -0.9    -0.9    -0.8    -0.8    -0.8    -0.8    -0.7    -0.8    -0.9    -0.9    -0.8    -0.8    -0.8    -0.7    -0.7    -0.7    -0.7    -0.6    -0.7    -0.7    -0.7    -0.7    -0.7    -0.7    -0.6    -0.6    -0.6    -0.6    -0.5
                                Traj    4    0.0    0.1    0.1    0.1    0.1    -0.1    -0.1    -0.0    0.0    0.2    0.1    -0.0    0.0    0.0    -0.3    -0.1    -0.1    -0.0    -0.0    0.1    0.1    0.2    0.3    0.4    0.3    0.4    0.5    0.5    0.4    0.6    0.5    0.5    0.3    0.2    0.3    0.3    0.3    0.3    0.3    0.5    0.6    0.6    0.7    0.7    0.8    0.8    0.7    0.6    0.6    0.5    0.4    0.5    0.5    0.6    0.5    0.4    0.5    0.4    0.4    0.5    0.5    0.6    0.7    0.6    0.6    0.6    0.6    0.7    0.8    0.8    0.8    0.7    0.7    0.8    1.0    0.9    0.8    0.8    0.8    0.9    0.9    0.8    0.7    0.8    0.8    0.8    0.6    0.6    0.2    0.2    0.2    0.2    0.4    0.3    0.3    0.4    0.5    0.6    0.4    0.4    0.4
                                Traj    5    0.0    0.0    0.1    0.2    -0.0    -0.1    -0.2    -0.0    0.2    0.2    0.5    0.5    0.4    0.2    0.2    0.2    0.1    0.0    -0.0    -0.1    -0.1    -0.0    0.0    -0.1    -0.1    -0.2    -0.3    -0.3    -0.1    -0.1    -0.3    -0.4    -0.5    -0.4    -0.4    -0.4    -0.2    -0.2    -0.1    -0.3    -0.3    -0.2    -0.3    -0.2    -0.1    -0.0    -0.1    -0.0    0.0    -0.1    -0.2    -0.1    -0.1    -0.1    0.0    0.2    0.3    0.3    0.4    0.4    0.6    0.6    0.6    0.7    0.6    0.5    0.6    0.5    0.5    0.3    0.3    0.1    0.1    0.1    0.1    0.2    0.2    0.1    -0.0    -0.0    -0.4    -0.3    -0.2    -0.0    -0.1    0.1    0.1    0.1    0.0    0.0    0.2    0.1    0.3    0.3    0.3    0.3    0.4    0.4    0.5    0.5    0.8
                                Traj    6    0.0    0.0    0.2    -0.0    0.1    0.0    0.0    0.1    0.0    -0.1    -0.1    -0.1    -0.2    -0.3    -0.3    -0.1    -0.1    -0.2    -0.1    -0.1    -0.1    -0.2    -0.2    -0.3    -0.5    -0.5    -0.4    -0.5    -0.5    -0.5    -0.4    -0.4    -0.4    -0.2    -0.1    -0.2    -0.2    -0.0    0.0    0.0    -0.1    -0.0    -0.1    -0.3    -0.1    -0.2    -0.4    -0.3    -0.3    -0.4    -0.5    -0.5    -0.7    -0.6    -0.8    -0.8    -0.9    -1.1    -0.9    -1.2    -1.4    -1.6    -1.6    -1.4    -1.4    -1.6    -1.6    -1.4    -1.4    -1.6    -1.4    -1.4    -1.5    -1.4    -1.6    -1.6    -1.6    -1.7    -1.7    -1.6    -1.6    -1.8    -1.8    -1.9    -2.0    -2.0    -2.1    -2.3    -2.3    -2.5    -2.6    -2.7    -2.5    -2.6    -2.6    -2.4    -2.7    -2.5    -2.6    -2.5    -2.5
                                Traj    7    0.0    0.0    0.0    0.0    0.3    0.3    0.4    0.3    0.3    0.2    0.1    0.1    -0.1    -0.0    -0.1    -0.1    -0.1    -0.2    -0.0    0.1    -0.0    0.1    0.1    0.1    -0.0    0.1    0.0    0.0    -0.0    -0.1    -0.1    -0.1    -0.2    -0.1    0.1    0.1    0.0    0.0    0.0    -0.1    -0.1    -0.0    0.1    0.2    0.1    0.1    0.1    -0.1    -0.2    -0.1    -0.0    -0.1    0.0    0.1    0.1    0.2    0.1    0.3    0.2    0.3    0.2    0.3    0.2    0.3    0.2    0.2    0.3    0.1    0.0    0.1    0.0    0.0    -0.1    -0.1    0.0    0.0    0.0    0.0    0.1    0.1    0.1    0.1    0.1    -0.0    -0.0    -0.0    -0.0    -0.1    -0.2    -0.2    -0.3    -0.4    -0.4    -0.3    -0.4    -0.5    -0.6    -0.7    -0.8    -0.6    -0.7
                                Traj    8    0.0    0.1    0.2    0.3    0.3    0.3    0.3    0.4    0.4    0.4    0.2    0.4    0.4    0.4    0.4    0.5    0.6    0.5    0.5    0.5    0.3    0.4    0.4    0.3    0.3    0.1    -0.0    0.2    0.0    -0.1    -0.1    -0.1    -0.1    -0.2    -0.3    -0.1    -0.0    -0.1    -0.1    0.1    0.2    0.2    0.3    0.2    0.1    0.2    0.1    0.1    0.0    -0.0    -0.2    -0.5    -0.5    -0.6    -0.5    -0.5    -0.4    -0.6    -0.8    -0.7    -0.7    -0.7    -0.6    -0.7    -0.7    -0.6    -0.8    -0.8    -0.5    -0.8    -0.9    -0.9    -1.0    -1.0    -0.8    -0.9    -0.9    -0.8    -0.8    -1.0    -0.9    -0.7    -0.9    -1.1    -1.0    -0.9    -0.8    -0.8    -0.6    -0.5    -0.3    -0.2    -0.3    -0.4    -0.3    -0.1    -0.2    -0.2    -0.2    -0.3    -0.4
                                Traj    9    0.0    0.0    -0.2    -0.2    -0.0    0.1    0.1    0.1    0.1    0.1    -0.0    -0.1    -0.1    -0.2    -0.2    -0.3    -0.3    -0.4    -0.5    -0.4    -0.2    -0.2    -0.2    -0.0    0.1    0.2    -0.0    -0.1    -0.3    -0.2    -0.2    -0.2    -0.1    0.0    0.2    0.2    0.2    0.4    0.4    0.5    0.5    0.5    0.5    0.4    0.4    0.5    0.3    0.3    0.2    0.2    0.1    0.1    -0.2    -0.2    -0.3    -0.4    -0.5    -0.5    -0.6    -0.7    -0.6    -0.6    -0.7    -0.4    -0.5    -0.3    -0.2    -0.2    -0.1    -0.2    -0.1    -0.1    -0.1    -0.2    -0.3    -0.4    -0.5    -0.6    -0.6    -0.6    -0.6    -0.5    -0.5    -0.4    -0.3    -0.2    -0.1    -0.1    -0.1    -0.1    -0.1    -0.2    -0.3    -0.3    -0.2    -0.1    0.0    0.1    0.1    0.2    0.2
                                Traj    10    0.0    0.1    0.1    -0.0    0.1    0.1    0.1    0.3    0.4    0.5    0.5    0.6    0.3    0.4    0.4    0.5    0.5    0.4    0.5    0.4    0.5    0.6    0.8    0.7    0.7    0.6    0.8    1.0    0.8    0.6    0.4    0.5    0.5    0.6    0.5    0.4    0.4    0.2    0.4    0.4    0.5    0.5    0.4    0.4    0.5    0.6    0.5    0.4    0.4    0.3    0.3    0.3    0.4    0.4    0.4    0.3    0.5    0.7    0.8    0.7    0.6    0.6    0.8    0.9    0.7    0.6    0.5    0.5    0.5    0.5    0.5    0.4    0.4    0.3    0.2    0.3    0.2    0.1    0.2    0.2    0.2    0.1    0.1    0.1    0.2    0.2    0.1    0.2    0.2    0.4    0.5    0.4    0.4    0.3    0.3    0.4    0.4    0.4    0.4    0.5    0.4
Standard
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excelbrownianmotion2021-fpt43jz1.xls exceloptionmodelnewmacexcelversion2021-gqsmibt2.xlsm hw2-xujmmmds.pdf hw2smiles-e54fcmyh.pdf
Answered 1 days After Mar 11, 2021

Solution

Sanjeev answered on Mar 13 2021
155 Votes
Microsoft Visual Basic for Applications
Module2 - 1

Function dOne(S, X, T, r, v, d)
dOne = (Log(S / X) + (r - d + 0.5 * v ^ 2) * T) / (v * (Sqr(T)))
End Function
Function NdOne(S, X, T, r, v, d)
NdOne = Exp(-(dOne(S, X, T, r, v, d) ^ 2) / 2) / (Sqr(2 * Application.WorksheetFunction.Pi()))
End Function
Function dTwo(S, X, T, r, v, d)
dTwo = dOne(S, X, T, r, v, d) - v * Sqr(T)
End Function
Function NdTwo(S, X, T, r, v, d)
NdTwo = Application.NormSDist(dTwo(S, X, T, r, v, d))
End Function
Function OptionPrice(OptionType, S, X, T, r, v, d)
If OptionType = "C" Then
OptionPrice = Exp(-d * T) * S *...
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