heston pricing using finite difference method [visual c++ express, gsl].mht

european_swaption_lmm.txt very nice implementation of complicated LMM. Informative for QF applicati

- 0.5*y*gamma*gamma* (V(i,j-1,k)-2*V(i,j,k)+V(i,j+1,k))/(dy*dy)
- r*x*(V(i+1,j,k)-V(i-1,j,k))/(2*dx)
- (alpha*(beta-y)-nu*gamma*y^0.5)*(V(i,j+1,k)-V(i,j-1,k))/(2*dy)
+ r*V(i,j,k) =3D 0

Step 2 : Group V(i,j,k) terms together
V(i,j,k)/dt
- 0.5*y*x*x* (-2*V(i,j,k))/(dx*dx)
- 0.5*y*gamma*gamma* (-2*V(i,j,k))/(dy*dy)
+ r*V(i,j,k)=20
- V(i,j,k-1)/dt=20
- 0.5*y*x*x* (V(i-1,j,k)+V(i+1,j,k))/(dx*dx)
- rho*gamma*y*x* (V(i+1,j+1,k) + V(i-1,j-1,k) - V(i+1,j-1,k) - =
V(i-1,j+1,k))/(4*dx*dy)
- 0.5*y*gamma*gamma* (V(i,j-1,k)+V(i,j+1,k))/(dy*dy)
- r*x*(V(i+1,j,k)-V(i-1,j,k))/(2*dx)
- (alpha*(beta-y)-nu*gamma*y^0.5)*(V(i,j+1,k)-V(i,j-1,k))/(2*dy) =3D 0


V(i,j,k)/dt
- 0.5*y*x*x* (-2*V(i,j,k))/(dx*dx)
- 0.5*y*gamma*gamma* (-2*V(i,j,k))/(dy*dy)
+ r*V(i,j,k)=20
- V(i,j,k-1)/dt
- 0.5*y*x*x* (V(i-1,j,k)+V(i+1,j,k))/(dx*dx)
- rho*gamma*y*x* (V(i+1,j+1,k) + V(i-1,j-1,k) - V(i+1,j-1,k) - =
V(i-1,j+1,k))/(4*dx*dy)
- 0.5*y*gamma*gamma* (V(i,j-1,k)+V(i,j+1,k))/(dy*dy)
- r*x*(V(i+1,j,k)-V(i-1,j,k))/(2*dx)
- (alpha*(beta-y)-nu*gamma*y^0.5)*(V(i,j+1,k)-V(i,j-1,k))/(2*dy) =3D 0

V(i,j,k)[1/dt - (0.5*y*x*x*(-2)/(dx*dx)) - =
0.5*y*gamma*gamma*(-2)/(dy*dy) + r ]
- V(i,j,k-1)/dt
- 0.5*y*x*x* (V(i-1,j,k)+V(i+1,j,k))/(dx*dx)
- rho*gamma*y*x* (V(i+1,j+1,k) + V(i-1,j-1,k) - V(i+1,j-1,k) - =
V(i-1,j+1,k))/(4*dx*dy)
- 0.5*y*gamma*gamma* (V(i,j-1,k)+V(i,j+1,k))/(dy*dy)
- r*x*(V(i+1,j,k)-V(i-1,j,k))/(2*dx)
- (alpha*(beta-y)-nu*gamma*y^0.5)*(V(i,j+1,k)-V(i,j-1,k))/(2*dy) =3D 0



V(i,j,k)[1/dt + y*x*x/(dx*dx) + y*gamma*gamma/(dy*dy) + r ]
- V(i,j,k-1)/dt
- 0.5*y*x*x* (V(i-1,j,k)+V(i+1,j,k))/(dx*dx)
- rho*gamma*y*x* (V(i+1,j+1,k) + V(i-1,j-1,k) - V(i+1,j-1,k) - =
V(i-1,j+1,k))/(4*dx*dy)
- 0.5*y*gamma*gamma* (V(i,j-1,k)+V(i,j+1,k))/(dy*dy)
- r*x*(V(i+1,j,k)-V(i-1,j,k))/(2*dx)
- (alpha*(beta-y)-nu*gamma*y^0.5)*(V(i,j+1,k)-V(i,j-1,k))/(2*dy) =3D 0


V(i,j,k)[1/dt + y*x*x/(dx*dx) + y*gamma*gamma/(dy*dy) + r ]
=3D 0.5*y*x*x* (V(i-1,j,k)+V(i+1,j,k))/(dx*dx)
+ rho*gamma*y*x* (V(i+1,j+1,k) + V(i-1,j-1,k) - V(i+1,j-1,k) - =
V(i-1,j+1,k))/(4*dx*dy)
+ 0.5*y*gamma*gamma* (V(i,j-1,k)+V(i,j+1,k))/(dy*dy)
+ r*x*(V(i+1,j,k)-V(i-1,j,k))/(2*dx)
+ (alpha*(beta-y)-nu*gamma*y^0.5)*(V(i,j+1,k)-V(i,j-1,k))/(2*dy)=20
+ V(i,j,k-1)/dt


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