A Rough Instantaneous Squared VIX Model for Term Structure and Option Pricing
Yang et al.
A model adding fractional memory to the VIX yields a Mittag-Leffler term structure and a semi-closed-form option price, and cuts out-of-sample option pricing errors, most at high volatility.
Source published · In the Daily Brief of 9 November 2026
Filed under Quantitative finance
The authors introduce fractional memory into a Markovian model of the instantaneous squared VIX. The term structure then decays according to a Mittag-Leffler function, and VIX options have a semi-closed-form price through an affine Fourier-Laplace transform, which allows a two-step calibration to term-structure indices and option quotes.
On daily data from January 2018 to June 2025, the model improves on the Markovian benchmark in fitting the term structure and reduces out-of-sample option pricing errors by 13.06% in mean squared error and 6.33% in mean absolute error. The gains are larger at short maturities and when the VIX is high.