Scenario-based stochastic model predictive control for dynamic option hedging

Bemporad, Alberto; Gabbriellini, Tommaso; Puglia, Laura; Bellucci, Leonardo

doi:10.1109/cdc.2010.5717004

Cited by 26 publications

(13 citation statements)

References 20 publications

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“…As shown in the works of Bemporad et al,() in the absence of transaction costs and under the lack of arbitrage, a way to achieve this is to minimize the variance of the hedging error

J ((), e false(T false)) = normalE ([], {((), e false(T false) - normalE ([], e false(T false)))}^{2})

by solving the one‐step‐ahead minimum variance problem

\min_{({}, u false(t false))} {Var}_{m false(t + 1 false)} ([], w ((), t + 1, m false(t + 1 false)) - p ((), t + 1, m false(t + 1 false)))

s.t. w ((), t + 1, m false(t + 1 false)) = false(1 + r false) w false(t false) + \sum_{i = 0}^{n} b_{i} ((), t, m false(t + 1 false)) u_{i} false(t false)

with respect to the portfolio composition u ( t ) at each trading date t T s .…”

Section: Dynamic Option Hedgingmentioning

confidence: 99%

“…Each scenario j has a probability π j of occurring, j =1,…, M , π j >0, π j ≤1,

\sum_{k = 1}^{M} π_{j} = 1

. Scenarios can be generated via Monte Carlo (MC) simulation, where

π^{j} = \frac{1}{M}

, or by discretizing a given probability density function that describes the disturbance process generating the asset prices . Note that, contrarily to multistage stochastic programming approaches that typically limit the number M of considered scenarios to only 2 or 3 to avoid the combinatorial explosion over the optimization horizon N , here M can be quite large without incurring into prohibitive computation efforts, as the prediction horizon is simply N =1.…”

Section: Dynamic Option Hedgingmentioning

confidence: 99%

“…In fact, numerical pricing engines must be used based on either MC simulation or other approximate methods such as the method described by Longstaff and Schwartz . See the works of Bemporad et al() for a comparison of different pricing methods. In particular, Bemporad et al showed that SMPC is superior to Δ‐hedging when dealing with exotic options and quite robust also to errors in the dynamical model of the market.…”

Section: Dynamic Option Hedgingmentioning

confidence: 99%

“…For the case without transaction costs, stochastic model predictive control (SMPC) approaches were proposed in the works of Bemporad et al() Stochastic model predictive control can be seen as a suboptimal way of solving a stochastic multistage dynamic programming problem. Rather than solving the problem for the entire remaining time span of the option life, a smaller problem is solved repeatedly from the current time step t up to a certain number N of time steps in the future by suitably remapping the condition at the future expiration date into a value at the predicted time step t + N .…”

Section: Introductionmentioning

confidence: 99%

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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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“…As shown in the works of Bemporad et al,() in the absence of transaction costs and under the lack of arbitrage, a way to achieve this is to minimize the variance of the hedging error

J ((), e false(T false)) = normalE ([], {((), e false(T false) - normalE ([], e false(T false)))}^{2})

by solving the one‐step‐ahead minimum variance problem

\min_{({}, u false(t false))} {Var}_{m false(t + 1 false)} ([], w ((), t + 1, m false(t + 1 false)) - p ((), t + 1, m false(t + 1 false)))

s.t. w ((), t + 1, m false(t + 1 false)) = false(1 + r false) w false(t false) + \sum_{i = 0}^{n} b_{i} ((), t, m false(t + 1 false)) u_{i} false(t false)

with respect to the portfolio composition u ( t ) at each trading date t T s .…”

Section: Dynamic Option Hedgingmentioning

confidence: 99%

“…Each scenario j has a probability π j of occurring, j =1,…, M , π j >0, π j ≤1,

\sum_{k = 1}^{M} π_{j} = 1

. Scenarios can be generated via Monte Carlo (MC) simulation, where

π^{j} = \frac{1}{M}

Section: Dynamic Option Hedgingmentioning

confidence: 99%

Section: Dynamic Option Hedgingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

“…Recent works by Bemporad et al [14]- [16], have shown that a stochastic model predictive control can perform extremely well, with performance approaching that of prescient MPC models for European options hedging.…”

Section: Introductionmentioning

confidence: 96%

Dynamic hedging of foreign exchange risk using stochastic model predictive control

Noorian

Leong

2014

2014 IEEE Conference on Computational Intelligence for Financial Engineering &Amp; Economics (CIFEr)

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A risk management system for foreign exchange (FX) brokers is described. Stochastic model predictive control (SMPC) is used to reduce positions in foreign holdings over a receding horizon, while minimising a mean-variance cost function. Computation of the broker's position incorporates elements which model client flow, transaction costs, market impact, and exchange rate. Using both synthetic and historical data, the technique is shown to outperform two simple hedging strategies on a risk-cost Pareto frontier. Prediction of client and market behaviour are shown to further enhance the hedging outcome.

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Applications of MPC to Finance

Primbs

2018

Handbook of Model Predictive Control

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Scenario-based stochastic model predictive control for dynamic option hedging

Cited by 26 publications

References 20 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

Dynamic hedging of foreign exchange risk using stochastic model predictive control

Applications of MPC to Finance

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