Dispensing with optimal control: a new approach for the pricing and management of share buyback contracts

Paper: arXiv 2404.13754

Authors: Bastien Baldacci, Philippe Bergault, Olivier Guéant

Abstract

This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state spaces and the intricacies of selecting appropriate risk penalty or risk aversion parameter. Our methodology applies optimized heuristic strategies to maximize the contract’s value. The computation of this value utilizes classical methods typically used for pricing path-dependent options. Additionally, our approach naturally leads to the formulation of a $Δ$-hedging strategy and disentangles therefore the repurchase strategy from the hedging of the payoff.

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 practical and innovative alternative to standard stochastic optimal control for share buyback contracts by employing optimized heuristic strategies combined with path-dependent option pricing techniques. It successfully decoupling the repurchase execution from delta-hedging, though empirical validation on real-market execution datasets remains somewhat limited.

Research Flowchart

  flowchart TD
    A[Research Goal: Overcome optimal control limitations in pricing & managing share buybacks] --> B[Inputs: Contract Specs, Market Data & Path-Dependent Option Framework]
    B --> C[Formulate & Optimize Heuristic Repurchase Strategies]
    C --> D[Compute Contract Value via Path-Dependent Option Pricing]
    D --> E[Derive Delta-Hedging Strategy from Option Value]
    E --> F[Outcome: Disentangled repurchase & hedging with efficient high-dimensional pricing]