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Deep Hedging for Deep OTM Options: A Multi-Asset Approach in Bates Jump-Diffusion Environments

To run simulations refer to public_api.py, main_grid_search and main_optimal.py

TL;DR

  • What this is: Reinforcement Learning is really popular atm because of its use in training LLMs. This project creates a simple model that learns how to do a single task (delta-hedging) really well.
  • Why this matters: Existing solutions struggle with extreme and sudden events ("jumps") that stem from dramatic market news. This is common in crypto and simulated with "jump-diffusion" processes. Additionally, traditional financial models break down with deep OTM options.
  • Why this is cool: This model learns to adapt its position without having to make over-constraining assumptions, outperforming traditional delta-hedging strategies.

Abstract

Hedging remains an ever-complicating problem in the financial securities industry, especially for deep out-of-the money (OTM) options where traditional models fail. We present a framework for hedging a portfolio of deep OTM European Calls and Puts, considering transactions costs, liquidity constraints, cross-correlations, and jumps. Under a market generated from a Bates stochastic volatility model, we find that a deep Reinforcement Learning (RL) agent significantly outperforms the classic Black–Scholes delta-neutral hedging strategy by 56.89% in VaR, 74.82% in CVaR, 76.79% in max drawdown, 89.41% in P&L, and 81.62% in utility.

Findings

First, we answer our initial topic question by establishing that deep hedging can be effectively calibrated to cryptocurrency markets, which serve as excellent proxies for extreme market conditions. Second, by incorporating cross-correlations, in addition to transaction costs and liquidity constraints, our framework addresses real trading limitations that are often ignored in theoretical models. Third, our approach demonstrates that neural networks can learn optimal hedging strategies that adapt to cross-asset correlations and sudden market jumps without relying on distributional assumptions.

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