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

Trading
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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.

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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,
• d2 = d1 – (vol * sqrt(t))
• d1 = [ ln(S0 / X) + t(r – q + ((vol^2) / 2)) ] / [ vol * sqrt(t) ]
• S0 = underlying price
• X = strike price
• vol = implied volatility (or your expectation of volatility)
• r = interest rate (annualized)
• t = time until expiration expressed as days / 365 (or trading days in a year)
• q = dividend yield of the underlying

If you use the strike price, then this formula will give you the market’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 market’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!

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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

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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.

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Thanks. Helps a lot!

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6

Hey Mike!

Any idea on how do we get this PoP for a strategy? Say with 2 or more legs?
Like how can we get combined dual delta?

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Hi @Tejas_MD

It is the same formula but with a slight change to the input value (which will vary by strategy). To recap from above:

  • To get the probability of the underlying being at or above the strike price: Use the strike price as the value for “X” in the formula
  • To get the probability of the underlying being at or above the breakeven point (PoP): Use the breakeven price as the value of “X”

The breakeven price will vary by strategy. For instance, a long call will have a breakeven of the strike price + premium. A long put will be the strike price - premium. For a combo strategy, you use the net or total premium.

For a bull call spread, you calculate the breakeven point by adding the “net premium” (long call debit - short call credit) to the strike price. This sum will be the value of “X”.

For a strategy like a straddle, you use the total premium (call + put) and add that to the strike price to obtain the upper breakeven point. Using this value as “X”, will provide the PoP for the strategy being profitable on the upside. To understand the PoP on the downside movement, you would subtract the total premium for the strike price to calculate the lower breakeven point. However, you would use the Put Dual Delta formula.

Put Dual Delta = (N(d2) - 1) * -e ^ (-qt)

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hello mike, i have one query …like we have 2 or more breakeven in that case how to calcul POP? like bear butterfly/bear condor?

thank you in advance for your support.

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Hi @firoz_quraishi -
When you start getting into 3+ leg strategies, you use a combination of what I’ve described above. For instance, an iron condor is 2 spreads: a bear call spread and a bear put spread. You are correct, there will technically be 2 POPs because the probability of profit is associated with a breakeven point. If there are two breakeven points, there are two POPs.

Even though there are two POPs, it may be more practical to think in terms of only one POP for the holistic strategy. You can either:
a) Average the two POPs assuming that the underlying is at the midpoint of the strategy’s strikes.
b) Take the higher POP value if the underlying’s position is favoring one breakeven point over the other. For example, if you have a 95-105 strangle and the underlying is at 102, you will probably focus on the higher POP (the one associated with the long call).

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