Notes: The symbol t denotes the current time; t 0 denotes the starting date of averaging; t 1 denotes the ending date of averaging; and T denotes the option maturity. * t , (33) reduces to the reciprocal gamma approximation of Milevsky and Posner [1998].
NUMERICAL COMPARISONSThis section examines the performance of the approximations described in the previous section. The approximate distributions used have the property that Notes: The parameters and benchmark values are from Zhang [2001]. S t = 100, r = 9%, q = 0, t 0 = t = 0, and T = 0.08. N, SG, LN, SL, RG, and SRG exhibit the option values using normal, shifted gamma, lognormal, shifted lognormal, reciprocal gamma, and shifted reciprocal gamma approximations, respectively. RMSE and MAE are the root of mean-squared error and the maximum absolute error. Time exhibits the average computing time obtained by the Matlab package on Microsoft Windows XP and based on an Intel Pentium Dual CPU T2390 with 1.86GHz CPU and 3.00GB RAM.
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