I have just started applying Binomial-Lattice, however I am yet to fully understand few things. My questions are:
What is the concept of working backward (left side) from the values in terminal (farthest) nodes at the right side. Why do we need to do backward induction? I started my first node with some value
S, at say time
t=1, then all I need to know are the option values anywhere ahead of this time till the option expires. What is the need and meaning of the values obtained by backward induction and how are those different from forward induction?
Now if I apply backward induction, then the values I get at the starting node (the left most node) is far greater than the values at any other node. What does that mean?
Let's take this for example: I start with
S=1.5295e+009at the starting node, and then after using Binomial-Lattice and doing backward induction, I get
9.9708e+10at the starting node. Why has it increased this much and what does that imply? If I decrease my time step by two times, then I further get very high values like
The values that we get in each node as we move ahead of starting node (i.e. the values on the nodes right hand side to left most node) are the value analogues to Present Value (PV) at that time or Net Present Value (NPV)?
EDIT: This is my Matlab code for binomial lattice:
function [price,BLOV_lattice]=BLOV_general(S0,K,sigma,r,T,nColumn) % BLOV stands for Binomial Lattice Option Valuation %% Constant parameters del_T=T./nColumn; % where n is the number of columns in binomial lattice u=exp(sigma.*sqrt(del_T)); d=1./u; p=(exp(r.*del_T)-d)./(u-d); a=exp(-r.*del_T); %% Initializing the lattice Stree=zeros(nColumn+1,nColumn+1); BLOV_lattice=zeros(nColumn+1,nColumn+1); %% Developing the lattice for i=0:nColumn for j=0:i Stree(j+1,i+1)=S0.*(u.^j)*(d.^(i-j)); end end for i=0:nColumn BLOV_lattice(i+1,nColumn+1)=max(Stree(i+1,nColumn+1)-K,0); end for i=nColumn:-1:1 for j=0:i-1 BLOV_lattice(j+1,i)=a.*(((1-p).*BLOV_lattice(j+1,i+1))+(p.*BLOV_lattice(j+2,i+1))); end end price=BLOV_lattice(1,1);
EDIT 2 (an additional question): If the binomial lattice is giving me option PV's, and my PV's are supposed to decrease with time, then why does more than half of values in my terminal nodes show an increase in values than what I start with (
=S0). See the attached picture for values.