Quant finance Series of 6 51 min
Mean-Reverting VIX
Models the VIX as a mean-reverting process, prices its futures and options, and shows what one day's option chain can and cannot identify.
What you need A first-year calculus course. Every other idea is built on the page.
Start with Vol. I 2026
- I The Rubber Band What the VIX is, how mean reversion becomes an ODE and then a stochastic model of log VIX, and what 22 years of daily closes say about it.
- II Futures, Options and a Flat Smile How the log VIX model of Vol. I prices VIX futures and options, how parity reads futures off the option chain, and why its implied volatility smile is flat.
- III Jumps, Vol-of-Vol and the Fourier Trick How upward jumps and random vol-of-vol fatten the right tail of log VIX, and how Gil-Pelaez inversion of the characteristic function prices VIX options.
- IV Calibration, and What the Thesis Didn't Say How the thesis calibrated its VIX models, what it left unstated, a check of its 2011 parameter tables, and why one expiry cannot identify the reversion speed.
- V 2026, viz. VIX The thesis' calibration rerun on the Cboe VIX option chain of 29 September 2026: smile fits, held-out strikes, futures, tail odds and the term structure.
- VI Trading It, Honestly Five trades a fitted VIX smile suggests, checked against the 2026 results: one fear premium measured, one hedge ratio inverted, three ideas left unsupported.