How Does the Concept of “Probability of Exercise” in Options Trading Relate to the Birthday Paradox?

The probability of exercise is the chance an option will be profitable to execute. This is a measure of likelihood in a vast space of potential outcomes (asset price paths).

It relates to the birthday paradox in that both concepts deal with the counter-intuitive likelihood of a specific event (collision/profitability) occurring sooner than a simple linear calculation would suggest. Both highlight that in large spaces, the probability of a match or a specific outcome can increase rapidly.