# How to simulate a Merton Jump Diffusion process?

I am talking about the Merton Jump Diffusion model, on this page, where they give the following formula:

$$dS_t = \mu S_t dt + \sigma S_t dW_t + (\eta-1) dq$$

where $W_t$ is a standard brownian motion, and $dq$ is an independent Poisson process (its value is 1 with probability $\lambda dt$)

On that page you can find some example code. However, it does not match the formula. I want to simulate stock paths with the MJD model but I do not know how to do it. What formula do they use for their simulation?

I have looked up a lot of papers, but they just give general from of the model and say this is the result, but they do not explain how to simulation goes in detail. What formula I have to use and how to implement the model. I am really frustrated because I do not know how to do this.

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You just need to decide of an unit of time $dt$ and then start simulating the path.
$dW_t$ is simulated using a random normal value. In Excel $N\left(\mu, \sigma\right)$ would be simulated by NORMINV(rand(), mu , sigma).
The page you linked used a formula linking $S_t$ and $S_{t+\Delta t}$