Stock Buybacks: An Option-Based Mathematical Modeling Approach to Financial Decision-Making

Abstract

The share repurchase decision is strategic for large corporations, yet comparative studies integrating mathematical modeling, financial options, and portfolio optimization remain limited. This study addresses this gap by proposing a quantitative analysis of share repurchase decisions using multiple approaches. The research compares the profitability of a Brazilian bank’s share repurchase program with the allocation of the same capital into an efficient portfolio, constructed based on DEA BCC models, Markowitz, Monte Carlo simulation, and financial option theory. Binomial modeling and the Black-Scholes model are applied to value repurchase as a financial option, incorporating risk, flexibility, and volatility. Data were processed in Python using historical time series from B3. The results show that, in the analyzed scenario, the optimized portfolio financially outperforms repurchase, providing a more efficient alternative. The study offers practical and technical evidence to support complex corporate decisions in highly uncertain environments.