Paper: arXiv 2302.07996

Authors: Ali Fathi, Bernhard Hientzsch

Abstract

We consider two data-driven approaches to hedging, Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control, under a stepwise mean-variance objective. We compare their performance for a European call option in the presence of transaction costs under discrete trading schedules. We do this for a setting where stock prices follow Black-Scholes-Merton dynamics and the “book-keeping” price for the option is given by the Black-Scholes-Merton model with the same parameters. This simulated data setting provides a “sanitized” lab environment with simple enough features where we can conduct a detailed study of strengths, features, issues, and limitations of these two approaches. However, the formulation is model free and could allow any other setting with available book-keeping prices. We consider this study as a first step to develop, test, and validate autonomous hedging agents, and we provide blueprints for such efforts that address various concerns and requirements.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 5.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a solid comparative study between Reinforcement Learning and Deep Trajectory-based Stochastic Control in a controlled Black-Scholes environment with transaction costs. While the empirical evaluation is limited to simulated data as a baseline ‘sanitized’ environment, the mathematical formulation of the stepwise mean-variance objective is rigorous and well-structured.

Research Flowchart

  flowchart TD
    A[Research Goal: Compare RL vs Deep Trajectory Control for Stepwise Mean-Variance Hedging] --> B[Input Data: BSM Stock Dynamics & Option Book-keeping Prices with Transaction Costs]
    B --> C[Implement Data-Driven Agents: Reinforcement Learning & Deep Trajectory Stochastic Control]
    C --> D[Simulate Discrete Trading Schedules in Controlled Lab Environment]
    D --> E[Evaluate Performance: Hedging Efficiency & Model Limitations]
    E --> F[Outcome: Validation & Blueprints for Autonomous Hedging Agents]