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This paper proposes stochastic model predictive control as a tool for hedging derivative contracts (such as plain vanilla and exotic options) in the presence of transaction costs. The methodology combines stochastic scenario generation for the prediction of asset prices at the next rebalancing interval with the minimization of a stochastic measure of the predicted hedging error. We consider 3 different measures to minimize in order to optimally rebalance the replicating portfolio: a trade-off between variance and expected value of hedging error, conditional value at risk, and the largest predicted hedging error. The resulting optimization problems require solving at each trading instant a quadratic program, a linear program, and a (smaller-scale) linear program, respectively. These can be combined with 3 different scenario generation schemes: the lognormal stock model with parameters recursively identified from data, an identification method based on support vector regression, and a simpler scheme based on perturbation noise. The hedging performance obtained by the proposed stochastic model predictive control strategies is illustrated on real-world data drawn from the NASDAQ-100 composite, evaluated for a European call and a barrier option, and compared with delta hedging.

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One of the most challenging tasks for an energy producer is represented by the optimal bidding on energy markets. Each eligible plant has to submit bids for the spot market one day before the delivery time and bids for the ancillary services provision. Allocating the optimal amount of energy, jointly minimizing the risk and maximizing profits is not a trivial task, since one has to face several sources of stochasticity, such as the high volatility of energy prices and the uncertainty of the production, due to the deregulation and to the growing importance of renewable sources. In this paper the optimal bidding problem is formulated as a multi-stage optimization problem to be solved in a receding horizon fashion, where at each time step a risk measure is minimized in order to obtain optimal quantities to bid on the day ahead market, while reserving the remaining production to the ancillary market. Simulation results show the optimal bid profile for a trading day, based on stochastic models identified from historical data series from the Italian energy market.