Martingale 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.