Speeding Up Monte Carlo Pricing of Exotic Options

# Pricing Exotics: Monte-Carlo is too slow?


# Pricing Exotics: Monte-Carlo is too slow?












I want to price exotic options under the exponential VG model and Merton's model to compare both models.

To price exotics under Merton's model, I have written the code below. The output is the price of a Call option, Asian, Digital and Up and in Barrier Call option. However, the use of loops leads to a very slow computation. Is there a clever way to not use loops here? In case of the VG model, I can do it but in this case, I do not see it.

```
function [Call,Asian,Digital,UIBP] = ExoticPricingMerton(S0,K,mu,delta,lambda,sigma,r,q,Maturity,H)

ht = 1/252; %trading days
P = 10^3; %Number of simulations
grid = (0:ht:Maturity); 
N = length(grid);

omega = r-q-((1/2)*sigma^2+lambda*(exp(mu+(1/2)*delta^2)-1)); 

S = zeros(P,N);
S(:,1) = S0; 

for i=1:P
    for j=2:length(grid)
        N = poissrnd(lambda*ht);
        J = cumsum([0, normrnd(mu,delta,1,N)]); 
        Z = normrnd(0,1);
        S(i,j) = S(i,j-1)*exp(omega*ht + sigma*sqrt(ht)*Z + J(end));
    end 
end 

%European Call option
A = max(S(:,end)-K,0); 
Call = exp(-r*Maturity)*(1/P)*sum(A); 

%Asian option
A = max(mean(S,2) - K,0);
Asian = exp(-r*Maturity)*(1/P)*sum(A);

%Digital price
A = max(S(:,end) - K, 0)./(S(:,end)-K);
Digital = exp(-r*Maturity)*(1/P)*sum(A);

%Up-and-in out Barrier
A1 = (max(S,[],2)-H)./abs(max(S,[],2)-H);
A2 = max(A1,0);
A = (max(S(:,end)-K,0)).*A2;
UIBP = exp(-r*Maturity)*(1/P)*sum(A); 
end
```

Thanks!

## Answer by quant_dev (score 3)

https://quant.stackexchange.com/a/31726

You're using a wrong tool for the job. Write your Monte Carlo in a faster language (Java would probably suffice, if not than C++ which is standard for such things). Then you will be able to efficiently generate more than 1000 paths. In fact, doing Monte Carlo derivatives pricing with 1000 paths is worthless. Your results are, most probably, very inaccurate. Read a good book on Monte Carlo pricing before venturing further and wasting your time.

## Answer by Woraphon T (score 1)

https://quant.stackexchange.com/a/31723

I assume you are using MatLab.

You may consider pre-generating all 1,000 random numbers once before for-loop by exploiting array coding.

Another approach, have you ever tried using Quasi Monte Carlo?

Generating Quasi-Random Numbers

QMC ensures faster convergence and MatLab has functions that can generate quasi-random sequence very fast (a billion under a second).