Biased control-variate estimation

Schmeiser, Bruce W.; Taaffe, Michael R.; WANG, JIN

doi:10.1080/07408170108936824

Cited by 19 publications

(17 citation statements)

References 12 publications

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“…Example: A fixed lookback option pricing under the NIG model. Let the asset price follow exponential NIG process (13) NIG(α, β, δ). Thus, the asset price is given by Tables III lists the VRRs by the antithetic variate, the control variate X CV 1 , the control variate X CCV and the control variate X NCV with optimal parameters and 32 Tables I and II, we observe that both the option prices and the standard errors by all the methods are very close.…”

Section: Numerical Test Resultsmentioning

confidence: 99%

“…Option pricing under Lévy processes for asset prices is one example. If μ Y is "unknown", it is proposed to use highly correlated control Y if the cost to approximate μ Y (Schmeiser et al (2001)) or to simulate μ Y (Pasupathy et al (2012)) is relatively low. The former is called biased control variate (BCV) and the latter is called control variates using estimated control means (CVEMs).…”

Section: Control Variate Methodsmentioning

confidence: 99%

“…Assume that under an equivalent martingale measure P , the asset price under an NIG model is given by (13). Now we consider the case of a discrete fixed strike lookback call option.…”

Section: Lookback Option Pricing Under Nig Modelsmentioning

confidence: 99%

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Pricing Lookback Options under Normal Inverse Gaussian Model by Variance Reduction and Randomized Quasi-Monte Carlo Methods

Lai

Zhang

2014

2014 Seventh International Joint Conference on Computational Sciences and Optimization

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In this paper, we investigate the lookback option pricing problem under the exponential normal inverse Gaussian model for the underlying asset price by antithetic variate and control variate methods combined with the quasi-Monte Carlo methods. The payoff of the geometric Asian option and a random variate conditional on the geometric mean of asset prices are used as the control vartiates. Numerical results with various model parameters and strike prices show that variances are reduced by both the antithetic variate and control variate methods. The variance reduction ratios are significantly improved when quasi-Monte Carlo methods are combined. For example, the variance reduction ratios are more than 10 5 for the discrete fixed strike lookback options with 32 monitoring points.

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Section: Numerical Test Resultsmentioning

confidence: 99%

Section: Control Variate Methodsmentioning

confidence: 99%

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Pricing Lookback Options under Normal Inverse Gaussian Model by Variance Reduction and Randomized Quasi-Monte Carlo Methods

Lai

Zhang

2014

2014 Seventh International Joint Conference on Computational Sciences and Optimization

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“…In almost all cases we consider, the means of the control variates cannot be exactly computed and need to be estimated. The user can follow the Estimated/Biased Control Variate approach (see (Schmeiser, Taaffe, and Wang 2001), (Pasupathy et al 2008), (Emsermann and Simon 2002)) where the means of the control variates are approximated or estimated via Monte Carlo. Alternatively, the DataBase Monte Carlo (DBMC) implementation proposed in (Borogovac andVakili 2008, Borogovac andVakili 2009) can be used, where, again, the means of the control variates need to be estimated via Monte Carlo.…”

Section: Introductionmentioning

confidence: 99%

Control variates for sensitivity estimation

Borogovac

Sun

Vakili

2010

Proceedings of the 2010 Winter Simulation Conference

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We adapt a newly proposed generic approach to control variate selection to the problem of efficient estimation of sensitivity of financial security prices to model parameters, the so-called Greeks. We show that estimators based on pathwise and likelihood ratio methods can be cast in a general setting where generic control variates can be systematically defined for their estimation. In general, the means of such controls cannot be exactly calculated. One can use the Biased or Estimated Control Variates approach and estimate the means via simulation, or use the approach of DataBase Monte Carlo (DBMC) which also requires estimation of control means via simulation. We consider a parametric setting where price sensitivities need to be estimated repeatedly at multiple parameters. The fact that the same controls can be used for multiple estimation problems can justify the setup cost. The approach is illustrated via simple examples and preliminary computational results are provided.

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“…Related estimators using biased control variables are analyzed by Schmeiser et al (2001), though not specifically focused on discretization error. In their setting, the simulated model is assumed to be correct, and bias results from using a numerical approximation to E X , whereas in this example and the previous one E X is assumed known, but the simulated model has some error, and the value of c X is intended to reduce the error.…”

Section: Applicationsmentioning

confidence: 99%

Large Sample Properties of Weighted Monte Carlo Estimators

Glasserman

2005

Operations Research

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A general approach to improving simulation accuracy uses information about auxiliary control variables with known expected values to improve the estimation of unknown quantities. We analyze weighted Monte Carlo estimators that implement this idea by applying weights to independent replications. The weights are chosen to constrain the weighted averages of the control variables. We distinguish two cases (unbiased and biased), depending on whether the weighted averages of the controls are constrained to equal their expected values or some other values. In both cases, the number of constraints is usually smaller than the number of replications, so there may be many feasible weights. We select maximally uniform weights by minimizing a separable convex function of the weights subject to the control variable constraints. Estimators of this form arise (sometimes implicitly) in several settings, including at least two in finance: calibrating a model to market data (as in the work of Avellaneda et al. 2001) and calculating conditional expectations to price American options. We analyze properties of these estimators as the number of replications increases. We show that in the unbiased case, weighted Monte Carlo reduces asymptotic variance, and that all convex objective functions within a large class produce estimators that are very close to each other in a strong sense. In contrast, in the biased case the choice of objective function does matter. We show explicitly how the choice of objective determines the limit to which the estimator converges.

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Biased control-variate estimation

Cited by 19 publications

References 12 publications

Pricing Lookback Options under Normal Inverse Gaussian Model by Variance Reduction and Randomized Quasi-Monte Carlo Methods

Pricing Lookback Options under Normal Inverse Gaussian Model by Variance Reduction and Randomized Quasi-Monte Carlo Methods

Control variates for sensitivity estimation

Large Sample Properties of Weighted Monte Carlo Estimators

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