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

TL;DR

This paper presents a new heuristic-based methodology for pricing and managing share buyback contracts, avoiding the complexities of traditional optimal control approaches and enabling effective hedging strategies.

Contribution

It introduces a novel heuristic approach that simplifies the pricing and management of buyback contracts, bypassing high-dimensional optimal control challenges.

Findings

Effective heuristic strategies for buyback contract valuation

Natural formulation of $\Delta$-hedging strategies

Decoupling of repurchase and hedging strategies

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 $\Delta$-hedging strategy and disentangles therefore the repurchase strategy from the hedging of the payoff.