Robust Optimization for Options Pricing in the Brazilian Market: An Application to European and American Options on PETR4, VALE3 and ITUB4

This work replicates and extends the robust pricing approach of Bandi and Bertsimas [2014] for the Brazilian market. Return uncertainty is modeled using a polyhedral set derived from the Central Limit Theorem, and pricing is formulated as a robust linear optimization that minimizes the worst-case replication error. The implied risk aversion Γ(K) is calibrated via cubic regression on moneyness. We apply the methodology to PETR4, VALE3, and ITUB4 on the B3, with underlying-asset-class and liquidity filters. Out-of-sample mean absolute errors were R$0.024 for European Calls, R$0.017 for European Puts, and R$0.089 for American Puts. We show that the discrepancy in deep-ITM American Puts coincides exactly with the strikes whose quotes violate the no-arbitrage bound P(K) ≥ K − S0; excluding these points, the error drops to R$0.005–R$0.022, practically indistinguishable from that obtained for the European Put on the same strikes.