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

Abstract

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.

Nonlinear model predictive control of a radiative heating process with movable radiators

“…MPC, with its numerous variations, is a well established control method known for its generality in terms of formulation. In the past, it has been successfully applied, for instance, to the control of thermal power plants, 3 bioprocesses, 4 and even dynamic option hedging 5 . Given the success and versatility of the method, we expect similarly excellent results from an application of MPC to the heating process considered in the present work.…”

Minimization of Constraint Violation Probability in Model Predictive Control

“…where ỹr,k+1 = y r,k+1 + wk is less likely than y r,k+1 = y r,k+1 + w k and y r,k+1 − ỹr,k+1 2 > y r,k+1 − y r,k+1 2 (29) due to wk 2 > w k 2 . It follows that the larger the value y k+1 − y r,k+1 2 , the higher the probability of a large value y k+1 − y r,k+1 2 due to (28). Therefore, the larger y k+1 − y r,k+1 2 , the higher the probability of y k+1 − y r,k+1 2 ≥ c k .…”

“…Due to its ability to efficiently cope with environments subject to uncertainty, SMPC has become increasingly popular in applications such as process control [14], [24], energy control [25] and power systems [26], [27], finance [28], general automotive applications [29], as well as more specifically safety-critical applications, e.g., path planning [15] and autonomous driving [30]- [35]. However, the possible constraint violation and the resulting infeasibility of the optimization problem are limiting factors when designing an efficient SMPC algorithm in practice, especially in safety-critical applications.…”

Stochastic predictive control

“…The fifth contribution ventures into an application of stochastic MPC to hedging derivative contracts (such as plain vanilla and exotic options) in the presence of transaction costs. The authors employ the scenario approach for the prediction of asset prices at the next rebalancing interval and minimize a stochastic measure of the predicted hedging error.…”