Hedging Derivatives Under Incomplete Markets with Deep Learning

This thesis implements the framework for dynamic statistical hedging under incomplete markets of the derivatives. The framework requires only definition of the payoff function as a formula that translates the paths of base assets into a scalar value of derivative’s holder PnL, and everything else is processed in the end-to-end learning manner. The created holistic model returns weights for the hedging portfolio, which can be easily converted into the real market orders, deeming the process to be ready for practical implementation. The study creates a seamless approach to creating a hedging trading strategies in the market with frictions, attaining the general structure of the resulting framework. The approach of deep learning via direct gradient optimization, contrary to the previous studies in the area of reinforcement learning, is implemented. The paper derives the applicable custom loss for optimization, compares the framework’s results with both classical financial mathematics approach of delta-hedging via Black-Scholes and Heston models, and the reinforcement learning baselines of Soft-Actor Critic and Proximal Policy Optimization algorithms. The model backtesting is done on the real 1 minute market data of USDRUB and EURRUB bid-ask 500k VWAP prices for the period of 2017-2024, using the real interest rate curves, present at the moment. The results show 1% statistical significance for the best-attained baseline outperformance for the 30 minutes frequency of the replicating portfolio rebalancing, and 0.01% significance for 5 minutes rebalancing frequency. Moreover, for the purposes of the simplicity of adding arbitrary feature illustration, the pre-trained embeddings of the financial Telegram channels posts are added, which drives results of the baselines outperformance to the level of <<0.01% significance (133.68 t-Student statistic).