Backward Hedging for American Options with Transaction Costs

ArXiv ID: 2305.06805 “View on arXiv”

Authors: Unknown

Abstract

In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which is based on either a risk measure or the mean squared error of the hedging strategy at maturity. The proposed algorithm moves backward in time, determining, for each time-step and different market states, the optimal hedging strategy that minimizes the loss function at the time the option is exercised, by assuming that the strategy used in the future for hedging the liability is the one determined at the previous steps of the algorithm. The approach avoids machine learning and instead relies on classic optimization techniques, Monte Carlo simulations, and interpolations on a grid. Comparisons with the Deep Hedging algorithm in various numerical experiments showcase the efficiency and accuracy of the proposed method.

Keywords: Backward Hedging, American Options, Transaction Costs, Monte Carlo Simulations, Optimal Hedging Strategy, Options

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic calculus, convex risk measures, and optimization theory, indicating high mathematical complexity, while the method is validated through extensive numerical experiments, Monte Carlo simulations, and comparisons with Deep Hedging, demonstrating strong empirical implementation.

  flowchart TD
    A["Research Goal: <br>Hedge American Options w/ Transaction Costs"] --> B["Methodology: <br>Backward Hedging Algorithm"]
    B --> C["Input Data: <br>Monte Carlo Simulated Asset Paths"]
    C --> D["Computational Process: <br>Backward Time Iteration"]
    D --> E{"At Exercise Date: <br>Minimize Loss Function?"}
    E -- Yes --> F["Calculate Optimal Hedge <br>Classic Optimization"]
    E -- No --> G["Interpolate Hedge from Grid"]
    F --> H["Key Findings: <br>High Accuracy & Efficiency"]
    G --> H
    H --> I["Comparison: <br>Superior to Deep Hedging"]