Computational Finance Labs V and VI Solution

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Description

1. Consider the following American put option problem:

8

@V

+

1

2S2

@2V

+ (r )S

@V

rV = 0; (0; 1) (0; T ]; T > 0

@t

2

@S2

@S

>

<

>

: with suitable initial and boundary and free boundary conditions:

    1. Solve the transformed PDE y = yxx of the above IBVP by using the Backward-Time and Central Space (BTCS) Scheme and the Crank-Nicolson nite di erence scheme.

    1. Plot V (S; t) for T = 1; K = 10; r = 0:25; = 0:6; = 0:2, and the payo .

    1. Solve the problem by using x and , and x=2 and =2 and calculate the error between these two numerical solution. Plot the error.

    1. Also calculate the error mentioned above for di erent values of x=2 and t=2 and plot N versus the maximum absolute error.

  1. Consider the following American call option problem:

8

@V

+

1

2S2

@2V

+ (r )S

@V

rV = 0; (0; 1) (0; T ]; T > 0

@t

2

@S2

@S

>

<

>

: with suitable initial and boundary and free boundary conditions:

  1. Solve the transformed PDE y = yxx of the above IBVP by using the Backward-Time and Central Space (BTCS) Scheme and the Crank-Nicolson nite di erence scheme.

  1. Plot V (S; t) for T = 1; K = 10; r = 0:06; = 0:3; = 0:25, and the payo .

  1. Solve the problem by using x and , and x=2 and =2 and calculate the error between these two numerical solution. Plot the error.

  1. Also calculate the error mentioned above for di erent values of x=2 and t=2 and plot N versus the maximum absolute error.

1