Capturing Smile Dynamics with the Quintic Volatility Model: SPX, Skew-Stickiness Ratio and VIX
Paper introduces two-factor Quintic Ornstein-Uhlenbeck model to calibrate SPX/VIX volatility surfaces, skew-stickiness ratio and stylized facts.
What it examines
This paper introduces a two-factor Quintic Ornstein-Uhlenbeck model using polynomial volatility modeling to jointly calibrate SPX and VIX smiles while capturing the skew-stickiness ratio. The approach utilizes calibration, finite-difference methods, and quantization cubature to overcome limitations in existing volatility models.
What it concludes
The study shows that the two-factor model fits SPX and VIX volatility surfaces and SSR while reproducing key market stylized facts. Its accurate calibration and dynamic consistency offer promising applications in option pricing, hedging, risk management, and further research into volatility dynamics.
Evidence objects
The paper introduces a two-factor Quintic Ornstein--Uhlenbeck model that captures SPX and VIX volatility surfaces while aligning with the observed skew-stickiness ratio ($SSR$), marking a notable advance in derivative pricing.
key_findings bullet 1 · key_findings · validation V0
Surprisingly, the model utilizes a degree five polynomial combining two mean-reverting OU processes sharing a Brownian motion driver, successfully fitting both the SPX volatility smile and the $SSR$ term structure.
key_findings bullet 2 · key_findings · validation V0
The study presents a novel joint calibration method for SPX, VIX, and $SSR$, introducing advanced techniques like quantization cubature to enhance computational speed and robustness, supported by comprehensive numerical experiments.
key_findings bullet 3 · key_findings · validation V0
Introducing a novel two-factor $$\text{Quintic Ornstein-Uhlenbeck volatility model}$$, the paper innovatively calibrates both $SPX$ and $VIX$ volatility surfaces while fitting the skew-stickiness ratio. The approach leverages empirical facts including the $Zumbach\text{ effect}$, resolving limitations of previous models and promising substantial impact on derivative modeling research and offering fresh theoretical insights globally.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
Abstract: We introduce the two-factor Quintic Ornstein-Uhlenbeck model, where volatility is modeled as a polynomial of degree five based on the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian Motion, each mean-reverting at a different speed. We demonstrate that the Quintic model effectively captures the volatility surfaces of SPX and VIX while aligning with the skew-stickiness ratio (SSR… ▽ More We introduce the two-factor Quintic Ornstein-Uhlenbeck model, where volatility is modeled as a polynomial of degree five based on the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian Motion, each mean-reverting at a different speed. We demonstrate that the Quintic model effectively captures the volatility surfaces of SPX and VIX while aligning with the skew-stickiness ratio (SSR) across maturities ranging from a few days to over two years. Furthermore, the Quintic model shows consistency with key empirical stylized facts, notably reproducing the Zumbach effect. △ Less
Source row: 368 · abstract type: unknown