Closed-form solutions for VIX derivatives in a Legendre empirical model
Pricing of Securities
2025-05-22 v2 Risk Management
Abstract
In this paper, we introduce a data-driven, single-parameter Markov diffusion model for the VIX. The volatility factor evolves in with a uniform invariant distribution ensured by Legendre polynomials, mapped to the empirical distribution. We derive analytical series solutions for VIX futures and options using separation of variables to solve the Feynman-Kac PDE. Compared to the 3/2 model, our approach offers equal or superior accuracy and flexibility, providing an efficient, robust alternative for VIX pricing and risk management. Code and data are available at github.com/gagawjbytw/empirical-VIX.
Keywords
Cite
@article{arxiv.2309.08175,
title = {Closed-form solutions for VIX derivatives in a Legendre empirical model},
author = {Ying-Li Wang and Cheng-Long Xu and Ping He},
journal= {arXiv preprint arXiv:2309.08175},
year = {2025}
}