# No Probability in Greeks

In an interview, I was once told that I should not consider probability when talking about option greeks since from a mathematical point of view greeks have nothing to do with probability. That is of course true, from a mathematical point of view, but the way greeks are taught always takes into account the probability reasoning.

For example, in this website Volatility it says this:

A rise in the implied volatility of a call will decrease the delta for an in-the-money option, because it has a greater chance of going out-of-the-money, whereas for an out-of-the-money option, a higher implied volatility will increase the delta, since it will have a greater probability of finishing in the money.

Again, it is taking into account probability to explain vega. I understand that because I was also taught greeks through probability reasoning. Therefore, how can I understand greeks functioning without taking into account the probability reasoning? How would you explain the relationship vega vs delta without considering "chances of ending in the money"?

• Honestly I think it's wrong to say that Greeks have nothing to do with probabilities. The value of an option is the integral of the payoff over the probability weighted possibilities. Many Greeks come about by changing the probabilities of those various possible scenarios. 9f someone thinks about Greeks purely from the formulae, then great, but it's wrong to say that they have nothing to do with probabilities.
– will
Oct 21, 2021 at 23:34
• How can we say they’re unrelated to probabilities when the Gaussian CDF or PDF is present in almost all of them? (Sincere question) Oct 22, 2021 at 13:07
• To add to the brilliant comments and answers, the otm call logic given in the question's link is not really accurate either as shown here and here. At the end of the day, even looking at mathematical concepts is less objective as one would think, especially if it's concerning applied mathematics. Oct 29, 2022 at 21:43