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

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                <TD class=3Dhead align=3Dleft colSpan=3D2 =
height=3D18>Category:=20
                  C++&nbsp; : &nbsp;Heston pricing using finite =
difference=20
                method</TD></TR>
              <TR>
                <TD class=3Deven vAlign=3Dbottom align=3Dleft=20
                  width=3D"65%"><B>Submitter:</B>&nbsp;<A=20
                  =
href=3D"http://www.quantcode.com/userinfo.php?uid=3D2704">wald</A></TD>
                <TD class=3Deven align=3Dright=20
                  width=3D"35%"><B>Date:</B>&nbsp;2008/2/2</TD></TR>
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                  =
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mp;lid=3D419"=20
                  target=3D_blank><B>Asset Backed</B></A> <BR>
                  <DIV=20
                  style=3D"FLOAT: left; OVERFLOW: hidden; WIDTH: 234px; =
HEIGHT: 30px"><SPAN=20
                  style=3D"DISPLAY: block; FONT-SIZE: 10px; LINE-HEIGHT: =
13px">Heston=20
                  pricing using finite difference method</SPAN> =
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                  <BR><BR><BR><B>Description:</B>=20
                  <DIV style=3D"TEXT-ALIGN: justify">Calculates price of =
an=20
                  European put option using finite difference =
method.<BR>It uses=20
                  successive over relaxation technique to solve the =
system of=20
                  equations arising from this PDE:<BR><IMG alt=3D""=20
                  =
src=3D"http://www.quantcode.com/uploads/img47a435b0ac83b.jpeg"><BR><BR>Fo=
llowing=20
                  are the results I have obtained while comparing with =
<A=20
                  =
href=3D"http://www.quantcode.com/modules/mydownloads/singlefile.php?cid=3D=
9&amp;lid=3D417"=20
                  target=3D_blank>Heston Option Price using Monte carlo=20
                  simulation</A><BR><BR>
                  <DIV class=3DxoopsCode><CODE><PRE>
Strike	Put Price MC	Put price SOR
0.5	0.001823098	0.00200973
0.75	0.023056369	0.0225265
1	0.102600138	0.100706
1.25	0.259924474	0.259371
1.5	0.472687498	0.473383

</PRE></CODE></DIV><BR><BR>Input values used are:<BR>int=20
                  timesteps=3D10; //no of time steps<BR>int =
stocksteps=3D50; //no of=20
                  points in stock axis<BR>int volsteps=3D50; //no of =
points in=20
                  variance axis<BR><BR><BR><BR>Derivation of Finite =
difference=20
                  scheme for the PDE :<BR>
                  <DIV class=3DxoopsCode><CODE><PRE>
//*****  derivation of finite difference scheme  ***************

Step 1: subtitute finite difference formulas based on central difference =
scheme into the PDE
(V(i,j,k)-V(i,j,k-1))/dt=20
- 0.5*y*x*x* (V(i-1,j,k)-2*V(i,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)