Call ITM odds from a put ITM probability of 0.42

Question

A stock follows geometric Brownian motion. A European put and a European call on it share the strike $15$ and the same expiry. Under the risk-neutral measure, the put has a $0.42$ chance of finishing in the money. What is the corresponding chance for the call?

Short answer

$0.58$ . Under a continuous distribution the stock ends exactly at the strike with probability zero, so exactly one of the two finishes in the money: $1-0.42=0.58$ .

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

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Lessons behind this question

Market Model and Risk-Neutral Valuation
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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