Discrete-time Variance-optimal Deep Hedging in Affine GARCH Models

Variance-optimal hedging in a discrete-time framework is a practical options strategy that aims to reduce the residual risk. It has been widely used in volatility trading desks. In this paper, we solve the variance-optimal hedging problem for affine GARCH models both semi-explicitly and through deep learning. Applying the Laplace transform method, we derive semi-explicit formulas for the variance-optimal hedging strategy and initial endowment. We also apply the Long Short-Term Memory (LSTM) recurrent neural network (RNN) architectures and solve for optimal hedging strategies under mean square error loss function with transaction costs. Numerical examples illustrate the hedging performance for different approaches, option styles, hedging frequencies and transaction costs.