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:
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.
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
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:
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.
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.
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