Chebyshev polynomial approximation to approximate partial differential equations



K

Sigma

t (yrs)

B&S

CC (2008)

40

0.2

0.0833

0.8403

0.838

40

0.2

0.3333

1.5221

1.472

40

0.2

0.5833

1.8812

1.802

45

0.2

0.0833

4.8399

4.837

45

0.2

0.3333

4.7804

4.771

45

0.2

0.5833

4.84

4.813

40

0.3

0.0833

1.2988

1.297

40

0.3

0.3333

2.4275

2.426

40

0.3

0.5833

3.0634

3.062

45

0.3

0.0833

4.9796

4.976

45

0.3

0.3333

5.5288

5.517

45

0.3

0.5833

5.9723

5.946

40

0.4

0.0833

1.7575

1.758

40

0.4

0.3333

3.3336

3.3335

40

0.4

0.5833

4.2473

4.246

45

0.4

0.0833

5.236

5.235

45

0.4

0.3333

6.3767

6.359

45

0.4

0.5833

7.1654

7.131

ABE

0.0151

Table 1

Column 4 shows the results using the Black and Scholes (1973) method.

Column 5 shows the results using our suggested method (Caporale and Cerrato - CC).

RMSE at the bottom of the table is the root mean square error.

16



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