# Challenge For The Stats Geniuses

Discussion in 'Advanced Probability and Statistics' started by cre8iveq, Jun 17, 2024.

1. ### cre8iveq

Joined:
Jun 17, 2024
Messages:
1
1
ok, I have a mathematical challenge. It's to do with options trading, but you shouldn't really need to know too much about options to solve it... just math.

ok, so let's say the price of stock XYZ is at $132. I sell a put option at a strike of$125 for a premium of $2. What this means is that if the price of XYZ at expiry (in 10 trading days) is over$125, I get to keep the $2. Anything below$125, and my profit/loss is $125 +$2 - End_Price.

I know the annualized volaility, let's say it's 50%, and from there we can work out the daily standard deviation. That is 0.5 / sqrt(252) - (because there are 252 trading days in a year) = 3.15%.

So here is the question...

How do I work out the expected value? i.e. If I did this trade a million times, how much money on average would I make or lose per time?

cre8iveq, Jun 17, 2024
mehul031215 likes this.