Asymptotic Behavior of the Fractional Heston Model

We consider the fractional Heston model originally proposed by Comte, Coutin and Renault [12]. Inspired by recent ground-breaking work on rough volatility [2, 6, 24, 26] which showed that models with volatility driven by fractional Brownian motion with short memory allows for better calibration of the volatility surface and more robust estimation of time series of historical volatility, we provide a characterisation of the shortand long-maturity asymptotics of the implied volatility smile. Our analysis reveals that the short-memory property precisely provides a jump-type behaviour of the smile for short maturities, thereby fixing the well-known standard inability of classical stochastic volatility models to fit the short-end of the volatility smile.

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