How to exactly calculate the 'Probability of profit'' metric on options

Trading
1

Hello, I wanted to know the formula for calculation of probability of profit (or Prob of ITM). Many platforms offer this metric but how is it actually calculated? I know for example, delta of a call option can be an approximation of probability of profit in %, but wanted to know the exact way it is calculated.

2

Hello @Tejas_MD

The probability of a strike being in-the-money and probability of profit are the same formula (derived from the Black-Scholes equation. The difference is the input value for the strike price.

Call Dual Delta = N(d2) * e ^ (-qt)
Where,
ā€¢ d2 = d1 ā€“ (vol * sqrt(t))
ā€¢ d1 = [ ln(S0 / X) + t(r ā€“ q + ((vol^2) / 2)) ] / [ vol * sqrt(t) ]
ā€¢ S0 = underlying price
ā€¢ X = strike price
ā€¢ vol = implied volatility (or your expectation of volatility)
ā€¢ r = interest rate (annualized)
ā€¢ t = time until expiration expressed as days / 365 (or trading days in a year)
ā€¢ q = dividend yield of the underlying

If you use the strike price, then this formula will give you the marketā€™s expectation for the probability of the strike being ITM. If you use the break-even price in place of strike price, then you will get the marketā€™s expectation for the probability of profit.

As a side note, our Ready-made Option Strategies tool in the Upstox app provides the probability of profit for option strategies. In addition, we are working to provide probability of profit and probability of strike moneyness as added features in our app and website. Stay tuned for more info on that!

Hope this helps!

2 Likes
3

Thanks Mike! understood. Looking forward to new features on Upstox! Just for clarification,
so if we neglect dividend yield, PoP would be norm.standard of d2 right?
and for put options, how do we go about it? is it just 100-PoP? and the same way to calculate for strategies as well right? Calculate combined Dual delta?

Thanks

1 Like
4

That is correct. If you ignore dividends, that term drops out.

For the put (both strike moneyness probability and PoP, the formula is: (N(d2) - 1) * (-e^-qt). So, it is just a slight modification. For both call and puts, this assumes that you are long the strategy.

1 Like
5

Thanks. Helps a lot!

3 Likes