Put ITM probability from a call delta of 0.67

Question

A European call with strike $K$ and expiry $T$ has delta $0.67$ . Roughly what is the probability that the put with the same strike and expiry finishes in the money?

Short answer

About $0.33$ . Using call delta as a rough proxy for the chance the call ends in the money, the put ends in the money in the complementary event, giving $1-0.67=0.33$ (strictly, delta is $N(d_1)$ rather than $N(d_2)$ , so this is an approximation).

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Greeks and Numerical Sensitivities
Taylor and Maclaurin Series
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets

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