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SRKX
SRKX
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Very Simple Log Return Correlated Stock simulation How to simulate 3 correlated stock processes following a GBM?

Suppose we have 3 stocks which follow GBMfollowing GBMs. 

We are given the distribution of the daily log returns which is multivariate normal. 

Suppose I want to sample the stock price tomorrow ($\Delta t = 1$ day). Could, could I just sample a return vector from this distribution and then say that the stock price tomorrow is $S_0 *exp(r_{sample}\Delta t)$.$S_0 \cdot \exp(r_\text{sample}\Delta t)$?

I've been arguing with my friend about this and he saysclaims I should multiply by $\sqrt(\Delta t)$$\sqrt{\Delta t}$? I don't understand his argument. 

Is there anything wrong with what I am doing here?

Very Simple Log Return Correlated Stock simulation

Suppose we have 3 stocks which follow GBM. We are given the distribution of the daily log returns which is multivariate normal. Suppose I want to sample the stock price tomorrow ($\Delta t = 1$ day). Could I just sample a return vector from this distribution and then say that the stock price tomorrow is $S_0 *exp(r_{sample}\Delta t)$. I've been arguing with my friend about this and he says I should multiply by $\sqrt(\Delta t)$? I don't understand his argument. Is there anything wrong with what I am doing here?

How to simulate 3 correlated stock processes following a GBM?

Suppose we have 3 stocks following GBMs. 

We are given the distribution of the daily log returns which is multivariate normal. 

Suppose I want to sample the stock price tomorrow ($\Delta t = 1$ day), could I just sample a return vector from this distribution and then say that the stock price tomorrow is $S_0 \cdot \exp(r_\text{sample}\Delta t)$?

I've been arguing with my friend about this and he claims I should multiply by $\sqrt{\Delta t}$? I don't understand his argument. 

Is there anything wrong with what I am doing here?

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Ryan J. Shrott
Ryan J. Shrott
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Very Simple Log Return Correlated Stock simulation

Suppose we have 3 stocks which follow GBM. We are given the distribution of the daily log returns which is multivariate normal. Suppose I want to sample the stock price tomorrow ($\Delta t = 1$ day). Could I just sample a return vector from this distribution and then say that the stock price tomorrow is $S_0 *exp(r_{sample}\Delta t)$. I've been arguing with my friend about this and he says I should multiply by $\sqrt(\Delta t)$? I don't understand his argument. Is there anything wrong with what I am doing here?