Simulating correlated stock prices

wbenard · July 5th, 2005, 8:02 pm

I am trying to simulate stock prices using GBM for a group of six stocks, each stock with its own assumption for expected return and volatility. Now I want the stockprices to be correlated, where correlation is based on historical correlation between stock returns. How can I model this? Is this done with a copula function?

Antonio · July 5th, 2005, 8:50 pm

You just need to replace the Brownian motion of each stock by the corresponding line in the product between the Cholesky decomposition of the correlation matrix and the matrix zith independent Brownian motions. There is already a thread (and surely mor than one) on this point.

wbenard · July 6th, 2005, 10:04 am

ok searched it and the technique is mostly clear to me, should be able to replicate that.another question is what the general consensus is on predicting stock price movements. I think GMB is the most used model for this, but are there any other popular methods to simulate future returns?

wbenard · July 6th, 2005, 11:59 am

i have estimated volatility and drift from historical daily data.now i determine the end value of the stock with the formulaSt = So * e^((u-(d^2/2))t+d*sqrt(t)*E))with E a random drawing from a standardized normal distribution.Now does it mather if I calculate the end value of the stock after lets say one year by: - using the formula with daily estimated vol and drift, and calculate daily prices for the coming year - use the formula but first rewrite daily vol and drift to yearly vol and drift, so effectively calculate the end value in one step.see attachted excelfile for examples.

Paolos · July 6th, 2005, 2:32 pm

QuoteOriginally posted by: wbenardNow does it mather if I calculate the end value of the stock after lets say one year by: - using the formula with daily estimated vol and drift, and calculate daily prices for the coming year - use the formula but first rewrite daily vol and drift to yearly vol and drift, so effectively calculate the end value in one step.It doesn't matter. The distribution of St is the same in both cases. (Obviously the second is faster)P.

wbenard · July 11th, 2005, 8:03 am

What do you think is the best estimator for mu, the drift, for stockprices?Base it on historical data (average historical return), or take the beta of the stock and calculate the CAPM expected return? Or even an other method?