Monte Carlo simulation comparison table: common random number method versus control variate method for Asian arithmetic option.
Estimated Delta of Asian arithmetic option by CRN method
Standard error by CRN method
Estimated Delta of Asian arithmetic option by control variate method
Standard error by control variate method
50
1
0.8682
0.1971
0.8806
0.0239
2
0.8140
0.1909
0.8351
0.0240
3
0.7795
0.1868
0.7783
0.0298
60
1
0.5630
0.1588
0.5687
0.0199
2
0.5875
0.1622
0.5466
0.0380
3
0.6030
0.1643
0.5969
0.0278
70
1
0.2405
0.1038
0.2514
0.0283
2
0.3668
0.1282
0.3569
0.0311
3
0.4228
0.1376
0.3492
0.0249
The table above is based on the Asian arithmetic option with the following parameters: , , sigma = 0.3, sample size , time step , and initial stock price shock epsilon = 0.1.
