Gamma Hedging

Deep Gamma Hedging ArXiv ID: 2409.13567 “View on arXiv” Authors: Unknown Abstract We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black–Scholes model then we find the network will successfully learn the Black-Scholes gamma hedging strategy, even if the dynamics of the underlying do not match the Black–Scholes model, so long as we choose a loss function that rewards coping with model uncertainty. Our results suggest that the reason gamma hedging is used in practice is to account for model uncertainty rather than to reduce the impact of transaction costs. ...

EX-DRL: Hedging Against Heavy Losses with EXtreme Distributional Reinforcement Learning ArXiv ID: 2408.12446 “View on arXiv” Authors: Unknown Abstract Recent advancements in Distributional Reinforcement Learning (DRL) for modeling loss distributions have shown promise in developing hedging strategies in derivatives markets. A common approach in DRL involves learning the quantiles of loss distributions at specified levels using Quantile Regression (QR). This method is particularly effective in option hedging due to its direct quantile-based risk assessment, such as Value at Risk (VaR) and Conditional Value at Risk (CVaR). However, these risk measures depend on the accurate estimation of extreme quantiles in the loss distribution’s tail, which can be imprecise in QR-based DRL due to the rarity and extremity of tail data, as highlighted in the literature. To address this issue, we propose EXtreme DRL (EX-DRL), which enhances extreme quantile prediction by modeling the tail of the loss distribution with a Generalized Pareto Distribution (GPD). This method introduces supplementary data to mitigate the scarcity of extreme quantile observations, thereby improving estimation accuracy through QR. Comprehensive experiments on gamma hedging options demonstrate that EX-DRL improves existing QR-based models by providing more precise estimates of extreme quantiles, thereby improving the computation and reliability of risk metrics for complex financial risk management. ...