Scenario-based stochastic model predictive control for dynamic option hedging

For a rather broad class of financial options, this paper proposes a stochastic model predictive control (SMPC) approach for dynamically hedging a portfolio of underlying assets. By employing an option pricing engine to estimate future realizations of option prices on a finite set of one-step-ahead scenarios, the resulting stochastic optimization problem is easily solved as a least-squares problem at each trading date with as many variables as the number of traded assets and as many constraints as the number of predicted scenarios. After formulating the dynamic hedging problem as a stochastic control problem, we test its ability to replicate the payoff at expiration date for plain vanilla and exotic options. We show not only that relatively small hedging errors are obtained in spite of price realizations, but also that the approach is robust with respect to market modeling errors.