Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints

We consider the joint SPX-VIX calibration within a general class of Gaussian polynomial volatility models in which the volatility of the SPX is assumed to be a polynomial function of a Gaussian Volterra process defined as a stochastic convolution between a kernel and a Brownian motion. By performing

Holy Grail Math 8 Rigor 8.5 ·  December 16, 2022

Capturing Smile Dynamics with the Quintic Volatility Model: SPX, Skew-Stickiness Ratio and VIX

We introduce the two-factor Quintic Ornstein-Uhlenbeck (OU) model, where volatility is modelled as a degree-five polynomial of the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian motion, each mean-reverting at a different speed. We demonstrate that the model effectively captures

Holy Grail Math 7.5 Rigor 8.5 ·  March 18, 2025

The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles

The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility model where the volatility process is a polynomial function of degree five of a single Ornstein-Uhlenbeck process with fast mean reversion and large vol-of-vol. The model is able to achieve remarkable joint fits of the SPX-VI

Holy Grail Math 8 Rigor 7.5 ·  December 21, 2022

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