Pricing and Calibration in the 4-Factor Path-Dependent Volatility Model

Guido Gazzani and Julien Guyon
Additional contact information
Guido Gazzani: UNIVR | DSE - Department of Economics [Verona] - UNIVR - Università degli studi di Verona = University of Verona
Julien Guyon: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique

Working Papers from HAL

Abstract: We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns. We discuss the influence of an additional parameter that unlocks enough volatility on the upside to reproduce the implied volatility smiles of S&P 500 and VIX options. This PDV model, motivated by empirical studies, comes with computational challenges, especially in relation to VIX options pricing and calibration. We propose an accurate neural network approximation of the VIX which leverages on the Markovianity of the 4-factor version of the model. The VIX is learned as a function of the Markovian factors and the model parameters. We use this approximation to tackle the joint calibration of S&P 500 and VIX options.

Keywords: Path-dependent volatility; Calibration of financial models; Neural networks; S&P 500/VIX joint calibration (search for similar items in EconPapers)
Date: 2024-12-24
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04855305

DOI: 10.2139/ssrn.4853419

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().