Paper: arXiv 2404.18761

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (19)

  1. Solving Linear Programs in the Current Matrix Multiplication Time (2021) — link
  2. Dual Pricing of American Options by Wiener Chaos Expansion (2018) — link
  3. Pricing American Options: A Duality Approach (2018) — link
  4. Deep hedging (2018) — link
  5. Optimal Stopping via Pathwise Dual Empirical Maximisation (2014) — link
  6. Optimal Dual Martingales, Their Analysis, and Application to New Algorithms for Bermudan Products (2011) — link
  7. Pricing and Hedging American-Style Options: A Simple Simulation-Based Approach (2010) — link
  8. Dual Valuation and Hedging of Bermudan Options (2010) — link
and 11 more
  1. Regression methods in pricing American and Bermudan options using consumption processes (2009) — link
  2. Sensitivities for Bermudan options by regression methods (2007) — link
  3. Monte Carlo valuation of American options (2002) — link
  4. Valuing American Options by Simulation: A Simple Least-Squares Approach (2001) — link
  5. Variance-Optimal Hedging in Discrete Time (1995) — link
  6. The Binomial Model and the Greeks (1994) — link
  7. Options Futures And Other Derivative Securities (2016)
  8. posted on any other website, including the author’s site. Please send any questions regarding this policy to permissions@informs.org. Pathwise Optimization for Optimal Stopping Problems (2012)
  9. A Primal-Dual Simulation Algorithm for Pricing Multi-Dimensional American Options (2001)
  10. Introduction to stochastic calculus applied to finance, by Damien Lamberton and Bernard Lapeyre (1998) — link
  11. Options, futures, and other derivative securities (1989) — link

0 of 19 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.