$30.00
Description
1. Consider the following American put option problem:

8
@V
+
1
^{2}S^{2}
@^{2}V
+ (r )S
@V
rV = 0; (0; 1) (0; T ]; T > 0
@t
2
@S^{2}
@S
>
<
>
: with suitable initial and boundary and free boundary conditions:


Solve the transformed PDE y = y_{xx} of the above IBVP by using the BackwardTime and Central Space (BTCS) Scheme and the CrankNicolson nite di erence scheme.



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



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



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


Consider the following American call option problem:

8
@V
+
1
^{2}S^{2}
@^{2}V
+ (r )S
@V
rV = 0; (0; 1) (0; T ]; T > 0
@t
2
@S^{2}
@S
>
<
>
: with suitable initial and boundary and free boundary conditions:

Solve the transformed PDE y = y_{xx} of the above IBVP by using the BackwardTime and Central Space (BTCS) Scheme and the CrankNicolson nite di erence scheme.

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

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

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