The short-expiry asymptotic lesson showed that diffusion models generate ATM skew growing at most as as . Empirical data for SPX weekly options shows skew growing faster — closer to . This lesson pins down the evidence, explains why jumps are the right mechanism to close the gap, and sets up the vocabulary needed for the Lévy process models developed in subsequent lessons.
Learning objectives. By the end of this note you should be able to:
- quantify the diffusion skew bound and the empirical short-dated skew excess;
- describe three types of gap risk (overnight gaps, earnings jumps, macro shocks) and their contribution to the short-dated smile;
- state the key properties that distinguish compound Poisson jumps from Brownian motion in the short-expiry limit.
In this lesson
- 1.1 The square-root law and its failure
- 1.2 Overnight gaps and the component
- 1.3 Why diffusion calibration cannot fix this
Before you start
- The Empirical Smile — Fat Tails, Skew, and the Limits of Black-Scholes
- Short-Expiry Vol Asymptotics — The Medvedev-Scaillet Expansion
The full lesson, with worked examples and exercise solutions, is for members.
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