On the Guyon-Lekeufack Volatility Model

2023/07/03 by Marcel Nutz, Nutz, Marcel, Andrés Riveros Valdevenito +1 · 2 citations
Economics, Econometrics and Finance · #60H10 #91G20 #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2307.01319

openalex publication_date 2023/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Guyon and Lekeufack recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylized facts. The instantaneous volatility is modeled as a linear combination of two processes, one is an integral of weighted past price returns and the other is the square-root of an integral of weighted past squared volatility. Each of the weightings is built using two exponential kernels reflecting long and short memory. Mathematically, the model is a coupled system of four stochastic differential equations. Our main result is the wellposedness of this system: the model has a unique strong (non-explosive) solution for all parameter values. We also study the positivity of the resulting volatility process and the martingale property of the associated exponential price process.

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