Rough Path-Dependent Volatility Models

Léo Parent ()
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Léo Parent: UP1 EMS - Université Paris 1 Panthéon-Sorbonne - École de Management de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne

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Abstract: This article introduces a family of rough path-dependent volatility (RPDV) models that encompass a wide range of modeling two major empirical features of volatility: its rough behavior and its path dependence. After presenting it in its general form and its connections to other existing models in the literature, we provide a Markovian multi-factor approximation of this family of RPDV models, building upon the works of Abi Jaber (2019). Then, our analysis focuses on some specifications of RPDV models interpretable from an economic point of view, leading to the formulation of different hypotheses about both asset price and volatility formation mechanisms.

Keywords: Volatility modeling; Path-dependent volatility; Rough volatility; Joint price and volatility dynamics (search for similar items in EconPapers)
Date: 2024-10-24
Note: View the original document on HAL open archive server: https://hal.science/hal-04751528v1
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