ArticleFinance & Economics
The Jump-Diffusion Smile
What option markets remember that Black-Scholes forgets
Jul 19, 2026 · 1 min read
Abstract
The Black-Scholes model prices every strike with one volatility, yet listed markets have priced a persistent skew since October 1987. This article walks through Merton's jump-diffusion extension, shows how a small probability of a large jump reproduces the observed smile, and explains why the smile's shape is best read as the market's memory of crashes.
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