Jump diffusion simulation problem

Hello,

I am trying to simulate jump diffusion processes with jump size distrubuted as a variable that can take only two values with probability p,1-p.

I want to leave as a input the number of simulated path but I am still having problem with the code. Do not consider the explanation since I started from another code.

Of course I will delete the input parameter which I set in the screen once it run properly

Can anyone help me?

Thanks

Answer 1

[TED MOSBY]

Hi Euginio,

You code seems to error out as I can see some pitfalls which I have mentioned below:

DW = sqrt(dt)*randn(1,N)

This line forces identical brownian shocks on all paths.

XS(i+1,k)

This is outside the for loop hence it overwrites all but the last i, leaving mostly zeros.

Nt = poissrnd(lambda*dt, nsim, N);
... if Nt(i) >= lb

You create Nt as nsim × N, then treat it like a 1-D vector (Nt(i))

Below is the vectorised implementation of your code:

function S = simulateJDBernoulli(mu,sigma,lambda,a,b,p,T,N,nsim,S0)
    dt   = T/N;
    nudt = (mu-0.5*sigma^2)*dt;
    sqdt = sqrt(dt);
    
    logS = zeros(N+1,nsim);
    logS(1,:) = log(S0);                
    
    for k = 1:N                           
        dW = sqdt*randn(1,nsim);          
        dN = poissrnd(lambda*dt,1,nsim);  
        
        % Jump magnitudes (vectorised)
        J  = (rand(1,nsim) < p).*a + (rand(1,nsim) >= p).*b;
        J  = J .* dN;                     % if dN>1 we add multiple jumps
        
        % One-step update in log-space
        logS(k+1,:) = logS(k,:) + nudt + sigma*dW + J;
    end
    
    S = exp(logS);                       
end

You can then call the function:

paths = simulateJDBernoulli(0.03,0.12,2.0,0.10,-0.05,0.6, ...
                            2.0,1000,50,100);
plot(0:1000,paths(:,1:5)), grid on
title('Five sample paths of Bernoulli jump–diffusion')

Output:

Hope this helps!