Notebook 5

Question 1

Create the function Brown()?

Answer 1

Question 2

Create a variable W_var = the variance of W over the paths and W_max, which is the Maximum W we see along each path/

Answer 2

Question 3

How would you plot this?

Answer 3

Question 4

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Question 5

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Question 6

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Question 7

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Question 8

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Question 9

How do we compare our SDE Euler function to the Black-Scholes formula?

Answer 9

Question 10

What is the function of Antithetic variance reduction, using SDE stepper function?

Answer 10

Question 11

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Question 12

Can use SDE_timestepper function

Answer 12

Question 13

Can use SDE_timestepper function

Answer 13

Question 14

Can use SDE_timestepper function

Answer 14

Question 15

What are the steps to create SDE_Basket_stepper () function?

Answer 15

Question 16

What is the code function for SDE_Basket_stepper()?

Answer 16

Question 17

What do we need to generate before testing the SDE Basket Stepper function against Black Scholes?

Answer 17

Question 18

How do you evaluate the SDE Basket Stepper function against Black Sholes when estimating a basket of European call options?

Answer 18

Question 19

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Question 20

What GBM_Euler() function?

Answer 20

Question 21

How do we verify the growth of the GBM_Euler() mean?

Answer 21

Question 22

What is the GBM_Milstein() function?

Answer 22

Question 23

How do we check of the increasing mean of GBM_Milstein()?

Answer 23

Question 24

What is CIR_Euler()?

Answer 24

Question 25

What is CIR_Milstein()?

Answer 25

Question 26

Weak Convergence GBM_Euler?

Answer 26

Question 27

Weak Convergence GBM_Milstein?

Answer 27

Needed 10**6 paths

Question 28

Weak Convergence of both GBM_Euler and GBM_Milstein?

Answer 28

Question 29

Strong Convergence of GBM_Euler?

Answer 29

Question 30

Strong Convergence of GBM_Milstein?

Answer 30

Question 31

Strong Convergence of GBM_Euler and GBM_Milstein?

Answer 31