Poisson distribution formula

Hello,

I am doing a study on black swan events. Which is events that are deviate normal expected behavior and is hard to predict, and in my case I will use Excel to generate a price index that has a black swan event. Meaning a crash or "boom" of 20-25% in one day.

When generating the magnitude of the boom or crash, I've used "RANDBETWEEN(20%,25%)".

However when calculating the probability of the jump I have to use a poisson distribution like POISSON.DIST(x,mean,cumulative).

The black swans I want to mimic are specifically of S&P 500. So I look at the number of times we had returns that are bigger than 5 standard deviations.

So would I then put "x= the number of days I have data on" and "mean = the number of days that are bigger than 5 standard deviations"?

Or something else?

Kind Regards,

Peter