A pure dual approach for hedging Bermudan options

ArXiv ID: 2404.18761 “View on arXiv”

Authors: Unknown

Abstract

This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a “purely dual” algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual pricing formula. The key is to rewrite the dual formula as an excess reward representation and to combine it with a strict convexification technique. The hedging strategy is then obtained by using a Monte Carlo method, solving backward a sequence of least square problems. We show convergence results for our algorithm and test it on many different Bermudan options. Beyond giving directly the hedging portfolio, the strength of the algorithm is to assess both the relevance of including financial instruments in the hedging portfolio and the effect of the rebalancing frequency.

Keywords: Bermudan Options, Hedging Portfolio, Dual Pricing Formula, Monte Carlo Method, Strict Convexification, Options (Derivatives)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper is highly mathematical, featuring dual representations, martingale decompositions, strict convexification, and convergence proofs; it also presents empirical testing with Monte Carlo methods, convergence analysis, and practical hedging experiments on multiple Bermudan options.

  flowchart TD
    A["Research Goal<br>Compute hedging portfolio<br>for Bermudan options"] --> B["Key Methodology<br>Pure Dual Approach<br>Strict Convexification"]
    B --> C["Data Inputs<br>Simulated asset paths<br>Risk-free rate info"]
    C --> D["Computational Process<br>Monte Carlo +<br>Backward Least Squares"]
    D --> E{"Key Outcomes"}
    E --> F["Direct Hedging Portfolio<br>Rebalancing Strategy"]
    E --> G["Validation of<br>Included Instruments"]
    E --> H["Assessment of<br>Rebalancing Frequency"]