From Stochastic to Rough Volatility: A New Deep Learning Perspective on Hedging

Abstract

The Black–Scholes model assumes that volatility is constant, and the Heston model assumes that volatility is stochastic, while the rough Bergomi (rBergomi) model, which allows rough volatility, can perform better with high-frequency data. However, classical calibration and hedging techniques are difficult to apply under the rBergomi model due to the high cost caused by its non-Markovianity. This paper proposes a gated recurrent unit neural network (GRU-NN) architecture for hedging with different-regularity volatility. One advantage is that the gating network signals embedded in our architecture can control how the present input and previous memory update the current activation. These gates are updated adaptively in the learning process and thus outperform conventional deep learning techniques in a non-Markovian environment. Our numerical results also prove that the rBergomi model outperforms the other two models in hedging.