# Probability of exercise in the Black-Scholes Model

What's the intuition behind the fact that the limit of $\mathcal{N}(d_2)$, i.e. the (risk-neutral) probability of exercise, in the Black-Scholes Model tends to $0$ when the volatility tends to infinity?

• Professor Nielsen of Columbia wrote what I would consider the canonical resource for intuition behind this in a BS world. – Jared Aug 8 '17 at 14:29

This is not very rigourous but I hope you get the idea, you could try plotting the lognormal pdf as $\sigma \to \infty$ for visual inspection.