Stopping times in Matlab

[figo]

Hi all,

for my project at uni I wanted to implement a modified binomial approach to price barrier options in Matlab.

In the first step I am approximating the price process by a step function Z with jumps at random times r_n. Z(t) jumps if and only if the price process Y changes by delta.

For a given accuracy delta we can define a step function according to:

r_0 = 0
r_n = inf{t \in [0,T] | t > r_(n-1), |Y(t) - Y(r_(n-1))| >delta}

Z(t) = \sum{n=0}{\infty} Y(r_n)*1_{r_n, r_(n+1)}(t)

I am struggling with the matlab implementation. I started learning Matlab 2 days ago and still are not really familiar with it.

I have problems to implement the stopping times. I want to be able to get the values r_n since i need to calculations with them at a later point.

Could you help me here?
Thank you!



I modelled the price process like this:

function X = binomialbarrier(delta,rate,vola,barrier,T,spot,K)

%Binomial Tree
N=90
t = (0:1:N)'/N; % t is the column vector [0 1/N 2/N ... 1]

W = [0; cumsum(randn(N,1))]/sqrt(N); % S is running sum of N(0,1/N) variables

t = t*T;
W = W*sqrt(T);

Y = log(spot)+(rate-(vola^2)/2)*t + vola * W; %geometric brownian motion

 

[Prashant.Kumar]

Judging from some code posted on wiki.
Does the following work?

dY = [0 diff(Y)];
jumps = (abs(dY) > delta);
Z = cumsum(Y .* jumps);

First line calculates the changes in Y.
(the left-concatenation of 0 is because diff(Y) has array length is one less than that of Y)
The second line is the signal of all indices at which Y jumped by more than dY in either direction.
The last line cumulatively adds up these jumps, using Y as the magnitude of the jump.
If you need to also switch whether the jump is positive or negative, instead use "cumsum(Y .* sign(dY) .* jumps)"

EDIT: Oops, necro'd, shame on me.