I am working on a problem and had a quick question. I understand that for Geometric Brownian Motion we use the formula:

$$X_{t_n} = X_{t_{n-1}} + \mu X_{t_{n-1}} \Delta t + \sigma X_{t_{n-1}} \epsilon_n \sqrt{\Delta t}$$

To my understanding this is for modeling non dividend paying stocks.

How should this formula be amended to allow for say a 2% continuous dividend?

  • 2
    $\begingroup$ What do you intend to do with these simulated paths? If this is for pricing, then under the risk-neutral measure your drift $\mu$ should actually be $r-d$ where $r$ is the risk-free rate, and $d$ the continuous dividend yield. $\endgroup$ – JejeBelfort Apr 10 at 7:41
  • $\begingroup$ Yes, it is for pricing. Thank you. $\endgroup$ – QFII Apr 10 at 18:37

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