Operational risk has been widely studied and there are international guidelines that provide procedures for the correct management of operational risk; however, this has not been studied from a corporate sustainability point of view. Therefore, this work seeks to find a way to model and optimize the impact of operational risks on corporate sustainability. The methodology used is based on the assignment of two distribution functions for the creation of a probabilistic model that allows quantifying the probability of occurrence (frequency) and the expected monetary impact (severity) on the sustainability variables (environmental, social, and economic). The result is a statistical convolution through Monte Carlo simulation which makes it possible to quantify aggregate losses to finally make an optimization process of the variables and estimate the financial impact. Therefore, this study extends the literature on risk quantification, proposing a stochastic model that quantifies and optimizes the operational risks that are related to corporate sustainability. The proposed model offers a practical way to quantify operational risks related to corporate sustainability.