Hedging and Pricing Structured Products Featuring Multiple Underlying Assets

Hedging a portfolio containing autocallable notes presents unique challenges due to the complex risk profile of these financial instruments. In addition to hedging, pricing these notes, particularly when multiple underlying assets are involved, adds another layer of complexity. Pricing autocallable notes involves intricate considerations of various risk factors, including underlying assets, interest rates, and volatility. Traditional pricing methods, such as sample-based Monte Carlo simulations, are often time-consuming and impractical for long maturities, particularly when there are multiple underlying assets. In this paper, we explore autocallable structured notes with three underlying assets and proposes a machine learning-based pricing method that significantly improves efficiency, computing prices 250 times faster than traditional Monte Carlo simulation based method. Additionally, we introduce a Distributional Reinforcement Learning (RL) algorithm to hedge a portfolio containing an autocallable structured note. Our distributional RL based hedging strategy provides better PnL compared to traditional Delta-neutral and Delta-Gamma neutral hedging strategies. The VaR 5% (PnL value) of our RL agent based hedging is 33.95, significantly outperforming both the Delta neutral strategy, which has a VaR 5% of -0.04, and the Delta-Gamma neutral strategy, which has a VaR 5% of 13.05. It also provides the hedging action with better left tail PnL, such as 95% and 99% value-at-risk (VaR) and conditional value-at-risk (CVaR), highlighting its potential for front-office hedging and risk management.

Hedging American Put Options with Deep Reinforcement Learning

This article leverages deep reinforcement learning (DRL) to hedge American put options, utilizing the deep deterministic policy gradient (DDPG) method. The agents are first trained and tested with Geometric Brownian Motion (GBM) asset paths and demonstrate superior performance over traditional strategies like the Black-Scholes (BS) Delta, particularly in the presence of transaction costs. To assess the real-world applicability of DRL hedging, a second round of experiments uses a market calibrated stochastic volatility model to train DRL agents. Specifically, 80 put options across 8 symbols are collected, stochastic volatility model coefficients are calibrated for each symbol, and a DRL agent is trained for each of the 80 options by simulating paths of the respective calibrated model. Not only do DRL agents outperform the BS Delta method when testing is conducted using the same calibrated stochastic volatility model data from training, but DRL agents achieves better results when hedging the true asset path that occurred between the option sale date and the maturity. As such, not only does this study present the first DRL agents tailored for American put option hedging, but results on both simulated and empirical market testing data also suggest the optimality of DRL agents over the BS Delta method in real-world scenarios. Finally, note that this study employs a model-agnostic Chebyshev interpolation method to provide DRL agents with option prices at each time step when a stochastic volatility model is used, thereby providing a general framework for an easy extension to more complex underlying asset processes.