S0

Numerical

algorithm

n = 200

Numerical

algorithm

n = 1000

Numerical

algorithm

n = 2000

Monte Carlo

Simulation

Times = 106

95.1

1.08754e−6

(1.131e−7)

1.17917e−6

(2.149e−8)

1.19107e−6

(9.588e−9)

0(−)

96

1.77950e−6

(1.769e−7)

1.922880e−6

(3.353e−8)

1.94145e−6

(1.496e−8)

3.33815e−6

(2.41542e−6)

100

3.93182e−6

(3.626e−7)

4.22590e−6

(6.850e−8)

4.22590e−6

(6.850e−8)

9.290592e−7

(8.43256e−7)

104

2.18637e−6

(2.171e−7)

2.36232e−6

(4.114e−8)

2.38510e−6

(1.835e−8)

0(−)

104.9

1.44651e−6

(1.499e−7)

1.56798e−6

(2.847e−8)

1.58375e−6

(1.269e−8)

4.638891e−6

(3.373127e−6)

CPU

397 ms

2072 ms

7114 ms

7984 s