Research paper on martingale property criteria for EFM signature volatility model released
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Dimitri Sotnikov and Adeline Viot published a research paper establishing a martingale criterion for exponentially fading memory (EFM) characteristic volatility models, extending the relevant conclusions of Abi Jaber, Gassiat, and Sotnikov in 2026. This model defines the volatility process through a linear functional of the EFM characteristics of time-augmented Brownian motion, featuring global well-posedness, complete non-Markovianity, and the existence of a stationary distribution, which can adapt to the initial forward variance curve. The study proves that, excluding trivial cases, the price process is a true martingale if and only if the truncation order is odd and the sign condition involving correlation parameters is satisfied.
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- arXiv q-finMartingale Property in the EFM Characteristic Volatility Model
This study establishes a martingale criterion for the exponentially fading memory (EFM) characteristic volatility model, extending related results from Abi Jaber, Gassiat, and Sotnikov (2026). The model defines the volatility process as a linear functional of the EFM characteristic of a time-augmented Brownian motion, featuring global well-posedness, fully non-Markovian dynamics, and a stationary distribution, and can accommodate initial forward variance curves. The study proves that, excluding trivial cases, the price process is a true martingale if and only if the truncation order is odd and a sign condition involving correlation parameters is satisfied.
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