Fast Hybrid Schemes for Fractional Riccati Equations (Rough is not so Tough)

Understand

We solve a family of fractional Riccati differential equations with constant (possibly complex) coefficients.

• These equations arise, e.g., in fractional Heston stochastic volatility models, that have received great attention in the recent financial literature thanks to their ability to reproduce a rough volatility behavior.
• We first consider the case of a zero initial value corresponding to the characteristic function of the log-price.
• Then we investigate the case of a general starting value associated to a transform also involving the volatility process.