A stochastic model predictive control approach to dynamic option hedging with transaction costs

Bemporad, Alberto; Puglia, Laura; Gabbriellini, Tommaso

doi:10.1109/acc.2011.5991205

Cited by 20 publications

(14 citation statements)

References 14 publications

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“…We test the 3 SMPC formulations for dynamic hedging defined, respectively, by Equations , 25, and 26 on a European plain vanilla call option and a barrier option with scenarios of stock and option prices generated according to Section 4. For the QP‐Var approach, we select α=0.25, as it was calibrated in the works of Bemporad et al using simulations of a lognormal stock model and assuming real market generating prices according to the same model (idealized nominal case). For the LP‐CVaR approach, we use β=95% in Equation 25.…”

Section: Hedging Resultsmentioning

confidence: 99%

“…We consider different performance measures (a trade‐off between variance and expected value of hedging error, conditional value at risk (CVaR), and the largest predicted hedging error) and show how the corresponding optimization problems can be easily solved via either quadratic or linear programming. A preliminary version of this work was presented in the conference paper of Bemporad et al, which we largely extend here by considering real‐world data in our results drawn from the NASDAQ‐100 composite and by proposing suitable scenario generation schemes to construct the stochastic optimization problems.…”

Section: Introductionmentioning

confidence: 89%

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Dynamic option hedging with transaction costs: A stochastic model predictive control approach

Plessen

Puglia

Gabbriellini³

et al. 2017

Intl J Robust & Nonlinear

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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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Section: Hedging Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 89%

Dynamic option hedging with transaction costs: A stochastic model predictive control approach

Plessen

Puglia

Gabbriellini³

et al. 2017

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let v j = max y j − r − α, 0 , the scenario-based SMPC problem can be redefined using the CVaR performance index [46]:…”

Section: Minimization Of Conditional Value At Risk (Lp-cvar)mentioning

confidence: 99%

Stochastic Model Predictive Fault Tolerant Control Based on Conditional Value at Risk for Wind Energy Conversion System

et al. 2018

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Abstract:Wind energy has been drawing considerable attention in recent years. However, due to the random nature of wind and high failure rate of wind energy conversion systems (WECSs), how to implement fault-tolerant WECS control is becoming a significant issue. This paper addresses the fault-tolerant control problem of a WECS with a probable actuator fault. A new stochastic model predictive control (SMPC) fault-tolerant controller with the Conditional Value at Risk (CVaR) objective function is proposed in this paper. First, the Markov jump linear model is used to describe the WECS dynamics, which are affected by many stochastic factors, like the wind. The Markov jump linear model can precisely model the random WECS properties. Second, the scenario-based SMPC is used as the controller to address the control problem of the WECS. With this controller, all the possible realizations of the disturbance in prediction horizon are enumerated by scenario trees so that an uncertain SMPC problem can be transformed into a deterministic model predictive control (MPC) problem. Finally, the CVaR object function is adopted to improve the fault-tolerant control performance of the SMPC controller. CVaR can provide a balance between the performance and random failure risks of the system. The Min-Max performance index is introduced to compare the fault-tolerant control performance with the proposed controller. The comparison results show that the proposed method has better fault-tolerant control performance.

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“…Theoretical advances are being made in a number of fields. Model Predictive Control (MPC) with stochastic weight models can be used [18] (most stochastic MPC approaches will consider only stochastic limits, not weights). On the other hand dynamic programming (usually involving quantization) and mixed integer algorithms can help to find the expected cost benefit of charging at specific times [19].…”

Section: Stochastic Pricesmentioning

confidence: 99%

Optimal Charging of EVs in a Real Time Pricing Electricity Market

Mody¹,

Steffen²

2013

SAE Int. J. Alt. Power.

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The idea of grid friendly charging is to use electricity from the grid to charge batteries when electricity is available in surplus and cheap. There are several ways of achieving this, for example using droop control, using night time electricity tariffs, or using smart metering. The goal is twofold: to avoid putting additional load on the electricity grid and power generation, and to reduce the cost to the consumer. This paper looks at the saving potential when charging an electric car using real time tariffs provided by a smart meter, using the Ameren tariffs in Illinois as an example. If prices are known in advance (day-ahead pricing), the optimization only requires picking the cheapest time slots for charging the battery. Further savings can be made by using real time prices that are not known in advance, but the optimization problem then depends on price prediction models, and it becomes much more difficult to solve. This paper presents a simple suboptimal approach, and it quantifies the potential improvements that could be made using more sophisticated price predictions.The result is that cost savings in the order of about 50 USD (1/3 of the electricity costs) are feasible if a fast charger is used using real time pricing. The scale of the savings is such that complex optimization strategies are not worthwhile, and for the foreseeable future simple solutions are expected to be more cost effective.

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A stochastic model predictive control approach to dynamic option hedging with transaction costs

Cited by 20 publications

References 14 publications

Dynamic option hedging with transaction costs: A stochastic model predictive control approach

Dynamic option hedging with transaction costs: A stochastic model predictive control approach

Stochastic Model Predictive Fault Tolerant Control Based on Conditional Value at Risk for Wind Energy Conversion System

Optimal Charging of EVs in a Real Time Pricing Electricity Market

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