Scenario

Model Parameters

OU Stochastic Correlation

BJ Stochastic Correlation

$\beta \left(0\right)$

${\mu }_{\beta }$

Strike

MC Price

Approx

Rel Error

MC Price

Approx

Rel Error

1

0

0.0

80

24.6479 (0.0506)

24.6472

−0.00%

24.6483 (0.0506)

24.6476

−0.00%

85

20.1757 (0.0489)

20.1426

−0.16%

20.1761 (0.0489)

20.1430

−0.16%

90

16.0172 (0.0463)

15.8726

−0.91%

16.0177 (0.0463)

15.8731

−0.91%

95

12.2973 (0.0423)

12.0183

−2.32%

12.2976 (0.0427)

12.0186

−2.32%

100

9.1217 (0.0384)

8.7531

−4.21%

9.1221 (0.0384)

8.7535

−4.21%

105

6.5438 (0.0335)

6.1505

−6.40%

6.5440 (0.0335)

6.1507

−6.39%

110

4.5422 (0.0285)

4.1780

−8.72%

4.5425 (0.0285)

4.1784

−8.71%

115

3.0571 (0.0236)

2.7525

−11.07%

3.0573 (0.0236)

2.7527

−11.07%

120

2.0019 (0.0192)

1.7642

−13.48%

2.0020 (0.0192)

1.7643

−13.47%

2

0

0.5

80

23.8150 (0.0498)

23.8102

−0.02%

23.8138 (0.0498)

23.8090

−0.02%

85

19.3741 (0.0480)

19.3008

−0.38%

19.3729 (0.0480)

19.2995

−0.38%

90

15.2703 (0.0453)

15.0387

−1.54%

15.2693 (0.0453)

15.0376

−1.54%

95

11.6337 (0.0416)

11.2522

−3.39%

11.6329 (0.0416)

11.2513

−3.39%

100

8.5556 (0.0371)

8.0958

−5.68%

8.5549 (0.0371)

8.0949

−5.68%

105

6.0753 (0.0321)

5.6123

−8.25%

6.0748 (0.0321)

5.6117

−8.25%

110

4.1717 (0.0271)

3.7607

−10.93%

4.1713 (0.0271)

3.7602

−10.93%

115

2.7783 (0.0223)

2.4455

−13.61%

2.7781 (0.0223)

2.4452

−13.61%

120

1.7961 (0.0180)

1.5425

−16.44%

1.7958 (0.0180)

1.5422

−16.44%

3

0

−0.5

80

25.4883 (0.0514)

25.4847

−0.01%

25.4900 (0.0514)

25.4864

−0.01%

85

20.9794 (0.0498)

20.9712

−0.04%

20.9811 (0.0498)

20.9728

−0.04%

90

16.773 (0.0473)

16.7199

−0.32%

16.7746 (0.0473)

16.7217

−0.32%

95

12.9872 (0.0439)

12.8213

−1.29%

12.9885 (0.0439)

12.8226

−1.29%

100

9.7213 (0.0396)

9.4572

−2.79%

9.7224 (0.0396)

9.4585

−2.79%

105

7.0384 (0.0348)

6.7269

−4.63%

7.0394 (0.0348)

6.7281

−4.63%

110

4.9338 (0.0298)

4.6267

−6.64%

4.9345 (0.0298)

4.6275

−6.63%

115

3.3552 (0.0249)

3.0870

−8.69%

3.3557 (0.0249)

3.0876

−8.68%

120

2.2245 (0.0204)

2.0091

−10.72%

2.2248 (0.0204)

2.0094

−10.72%

${\rho }_{\text{S}\beta }$

${\rho }_{\text{X}\beta }$

Strike

MC Price

Approx

Rel Error

MC Price

Approx

Rel Error

4

0.5

0.5

80

24.6494 (0.0506)

24.6487

−0.00%

24.6492 (0.0506)

24.6485

−0.00%

85

20.1723 (0.0489)

20.1386

−0.02%

20.1718 (0.0489)

20.1380

−0.18%

90

16.0182 (0.0463)

15.8726

−0.92%

16.0172 (0.0463)

15.8712

−0.92%

95

12.3098 (0.0427)

12.0310

−2.32%

12.3086 (0.0427)

12.0292

−2.32%

100

9.1403 (0.0383)

8.7727

−4.19%

9.1389 (0.0383)

8.7705

−4.20%