Option hedging using LSTM-RNN: an empirical analysis

Abstract

This paper proposes an optimal hedging strategy in the presence of market frictions using the Long Short Term Memory Recurrent Neural Network (LSTM-RNN) method, which is a modification of the method proposed in Buehler et al. (Deep hedging. Quant. Finance, 2019, 19(8), 1271–1291). The market frictions are transaction costs, liquidity constraints, trading limits and cost of funds. The loss function is a spectral risk measure. We first make an empirical analysis of the LSTM-RNN model of real option markets, which are the Asian market (domestic market 50 ETF option, Hong Kong Hang Seng Index Option, Nikkei Index Option), the North American market (S&P 500 Index Option) and the European market (FTSE 100 Index Option). The benchmark models are from Leland (Option pricing and replication with transaction costs. J. Finance., 1985, 40(5), 1283–1301), Boyle and Vorst (Option replication in discrete time with transaction costs. J. Finance, 1992, 47(1), 271–293) and Whalley and Wilmott (A hedging strategy and option valuation model with transaction costs. OCIAM Working Paper, Mathematical Institute, Oxford, 1993). Finally, we compare the results from the LSTM-RNN model with benchmark models involving transaction costs for both simulated market data generated by Geometric Brownian Motion (GBM) and the Heston model and real market data. The results show that the LSTM-RNN model outperforms benchmark models for low or medium volatility (<0.8), OTM moneyness and under a certain risk level (<80%) in the GBM market setting. For the 50ETF option market, the LSTM-RNN model outperforms benchmark models for ATM and under a certain risk level (<15%). For the HSI option market, the LSTM-RNN model outperforms benchmark models when transaction costs are smaller than 1.5%. For the Nikkei and S&P 500 option markets, the LSTM-RNN model always outperforms benchmark models. For the FTSE option market, the LSTM-RNN model outperforms benchmark models when moneyness is not too deeply ITM.