The PDE modelling the Asian option for the European arithmetic average strike call (for S 0; A 0; 0 t T ) is given by
@V
1
2
2
@2V
@V
@V
+
S
+ rS
+ S
rV = 0:
@t
@S2
2
@S
@A
e
By using the transformation V (S; A; t) = V (S; R; t) = S H(R; t); with R = A=S, transform the above PDE into the following form:
@H
1
@2H
@H
@t +
2 2R2 @R2 + (1 rR) @R = 0;
! 1
H=0;
for R
;
@H
@H
+
= 0;
for R = 0;
T
@t
@R
+
(
RT
)
1
H(RT;T) =
Solve the above transformed PDE by the following schemes:
Forward-Euler for time & central difference for space (FTCS) scheme.
Backward-Euler for time & central difference for space (BTCS) scheme.
Crank-Nicolson finite difference scheme with a suitable second-order approximation for the left boundary condition.
Plot the solution surfaces for K = 100; T = 0:2; r = 0:05; = 0:25 at different time levels.
1
