Martingality in EFM Signature Volatility Models

Dimitri Sotnikov () and Adeline Viot ()
Additional contact information
Dimitri Sotnikov: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, Engie Global Markets, ENGIE
Adeline Viot: ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay

Working Papers from HAL

Abstract: We establish a martingality criterion for the Exponentially Fading Memory (EFM) signature volatility model, extending the recent result of Abi Jaber, Gassiat, and Sotnikov (2026). In the proposed framework, the volatility process is given by a linear functional of the EFM signature of a time-augmented Brownian motion, which yields a globally well-behaved, fully non-Markovian volatility model admitting a stationary distribution. The stationary EFM signature volatility model is also covered by allowing for a random initial value of the signature. Moreover, the volatility process can be adjusted to the initial forward variance curve. For this model, excluding trivial cases, we prove that the price process is a true martingale if and only if the truncation order is odd and a sign condition involving the correlation parameter holds.

Keywords: EFM signature; stochastic volatility; martingality; Ornstein-Uhlenbeck (search for similar items in EconPapers)
Date: 2026-10-26
Note: View the original document on HAL open archive server: https://hal.science/hal-05838829v1
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-05838829v1/document (application/pdf)

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-05838829

Access Statistics for this paper

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