Simulate a time series of stock price using Monte-Carlo simulations

Hy everyone, I need to compute a time series of stock price assuming that they are driven by a random walk. What would be the best way to approach the problem, i.e. the right function to do so? I should replicate it 10.000 times (N=10.000).

thanks for the help.

[Rick Rosson]

The first thing you will need to do is to generate random numbers using a MATLAB function such as rand, randi, or randn. The choice of function and the way that you call it will depend on the statistical properties of the random walk. What type of probability distribution do you want to assume for each step of the random walk? What mean, variance, range, etc. do you plan on using?

[Alessandro]

the random walk has a standard normal distribution ~N(0,1) and I should use T random walks (from t=1,...T). Any other information? Thank you

[Rick Rosson]

Use the randn function.

[Rick Rosson]

A few additional points:

• Remember to put something in your code to prevent the stock price from falling below 0.
• Also, in the real-world, stock prices tend to drift higher over time, so the assumption of a zero mean is not realistic. The mean should be a positive number, although possibly quite small in relative terms. Furthermore, the size of the mean is usually proportional to the current price of the stock, as is the standard deviation.
• It might be interesting to consider the relative sizes of the mean versus the standard deviation of the net change per period.

Answer 1

[Rick Rosson]

Here is some code to get you started:

   N = 10000;
   P = nan(N,1);
   P(1) = ...

   for k = 2:N

       P(k) = P(k-1) + ...

   end

   figure;
   plot(P);