Significant Variance Reduction Research Articles

Exact simulation of the Hull and White stochastic volatility model

We show how to simulate exactly the asset price and the variance under the Hull and White stochastic volatility model. We derive analytical formulas for the Laplace transform of the time integral of volatility conditional on the variance level at the endpoint of the time interval and the Laplace transform of integrated variance conditional on both integrated volatility and variance. Based on these results, we simulate the model through a nested-conditional factorization approach, where Laplace transforms are inverted through the (conditional) Fourier-cosine (COS) method. Under this model, our approach can be used to generate unbiased estimates for the price of derivatives instruments. We propose some variants of the exact simulation scheme for computing unbiased estimates of option prices and sensitivities, a difficult task in the Hull and White model. These variants also allow for a significant reduction in the Monte Carlo simulation estimator's variance (around 93-98%) and the computing time (around 22%) when pricing options. The performances of the proposed algorithms are compared with various benchmarks. Numerical results demonstrate the faster convergence rate of the error in our method, which achieves an O(s−1/2) convergence rate, where s is the total computational budget, largely outperforming the benchmark.

Distributional Off-Policy Evaluation for Slate Recommendations

Recommendation strategies are typically evaluated by using previously logged data, employing off-policy evaluation methods to estimate their expected performance. However, for strategies that present users with slates of multiple items, the resulting combinatorial action space renders many of these methods impractical. Prior work has developed estimators that leverage the structure in slates to estimate the expected off-policy performance, but the estimation of the entire performance distribution remains elusive. Estimating the complete distribution allows for a more comprehensive evaluation of recommendation strategies, particularly along the axes of risk and fairness that employ metrics computable from the distribution. In this paper, we propose an estimator for the complete off-policy performance distribution for slates and establish conditions under which the estimator is unbiased and consistent. This builds upon prior work on off-policy evaluation for slates and off-policy distribution estimation in reinforcement learning. We validate the efficacy of our method empirically on synthetic data as well as on a slate recommendation simulator constructed from real-world data (MovieLens-20M). Our results show a significant reduction in estimation variance and improved sample efficiency over prior work across a range of slate structures.

1 Quantity or quality? Comparing objective and subjective participation measures to predict quality of life in aging msTBI.

Objective:Community reintegration and participation have been shown to be significantly correlated to improved Quality of Life (QoL) following moderate to severe traumatic brain injury (msTBI), yet these models often come with significant levels of unaccounted variability (Pierce and Hanks, 2006). Measures for community participation frequently employ objective measures of participation, such as number of outings in a week or current employment status (Migliorini et al., 2016), which may not adequately account for lifestyle differences, especially in aging populations. Less often integrated are subjective measures of an individual’s own belongingness and autonomy within the community (Heineman et al., 2011), also referred to as their participation enfranchisement (PE). The present study examines three questions pertinent to the potential clinical value of PE. First, do measures of objective participation significantly predict an individual’s PE ratings? Second, are both types of measures equally successful predictors of QoL for aging individuals with chronic-stage msTBI. Finally, would controlling for either objective or subjective integration ratings enable neurocognitive assessments to better predict QoL post injury?Participants and Methods:41 older-adults (M= 65.32; SD= 7.51) with a history of msTBI were included (M= 12.59 years post-injury;SD= 8.29) for analysis. Subjective community integration was measured through the Participation Enfranchisement Survey. The Participation Assessment with Recombined Tools-Objective (PART-O) provided the objective measurement of participation. Quality of life was assessed through the Quality of Life after Brain Injury (QOLIBRI). An estimate of neurocognitive performance was created through the Brief Test of Adult Cognition by Telephone (BTACT), which includes six domains including: verbal-learning and memory (immediate and delayed recall), working memory (digit-span backwards), reasoning (number sequencing), semantic fluency (category fluency), and processing speed (backwards counting). Performance on the BTACT, PE ratings, and PART-O scores were included as the dependent variables in stepwise, linear regression models predicting QoL ratings to assess the differential contribution of the dependent variables and potential interaction effects.Results:While both the PART-O (f(1,39)=5.52;p=.024,n2=.124) and the PE survey (f(1,39)=14.31 ;p<.001,n2=.268) significantly predicted QoL, the addition of PE in the PART-O model resulted in significant (20.9%) reduction in unaccounted variance. Further in the model controlling for PE, PART-O no longer provides a significant (p=.15) contribution to the model estimating QoL (f(2,38)=8.41; p=.001). Performance on the BTACT correlated with PART-O (p<.0001), but not PE (p=.13) ratings. Finally, across two models controlling for BTACT performance, PE (p=.002,partial n2=.23), but not PART-O (p=.28,partial n2=.031) contributed significantly to QoL predictions. No significant interactions between PART-O, PE, and/or BTACT were observed when added to any model.Conclusions:MsTBI impacts nearly every facet of an individual’s life, and as such, improving QoL post-injury requires a broad, yet well-considered approach. The objective ratings of participation, subjective PE, BTACT performance, all independently predicted quality of life in this sample. However, after controlling for neurocognitive assessment performance, PE was shown to independently contribute to quality of life, while the PART-O ratings no longer provided significant contribution. While community integration is a vital factor to consider for long-term rehabilitation, tailoring what “integration” means to the patient may hold significant potential to improve long-term quality of life.

Data-driven joint multi-objective prediction and optimization for advanced control during tunnel construction

This research develops a hybrid approach that integrates light gradient boosting machine (LightGBM) and non-dominated sorting genetic algorithm II (NSGA-II) to optimize the tunnel boring machine (TBM) performance during excavation. The TBM operational data are first extracted and meta-models are established to estimate the key TBM performance, including the penetration rate, over/under excavation ratio, and energy consumption. An optimization process is proposed by adopting NSGA-II and the technique for order preference by similarity to an ideal solution (TOPSIS) analysis to determine ideal operational parameters. The developed approach acts as a useful tool that assists tunnel construction automation and improves TBM performance under different in-situ conditions. Real data from a tunnel project in Singapore is utilized as a case study to examine the applicability and efficiency of the proposed approach. The results indicate that (1) The proposed meta-model provides reliable estimation with an average RMSE and MAE of 2.604mm/min and 3.402mm/min for TBM’s penetration rate(O1), 0.0211 and 0.0324 for over/under excavation ratio (O2), and 15.512kwh and 23.088kwh for energy consumption (O3), respectively. The prediction accuracy is better than the state-of-the-art methods; (2) The TBM’s performance can be optimized by the proposed approach with an average improvement of 33.14 %, 1.32 %, and 17.95 % for O1 to O3, respectively, and an overall improvement of 39.60 %; (3) The overall reliability of TBM operation improved after optimization with a significant reduction in data variance by 91.16 %, 76.92 %, and 97.35 % for O1 to O3, respectively. This paper contributes to proposing a novel method that integrates LightGBM with NSGA-II in resolving the complex TBM operation problem by considering the major performance indexes including excavation efficiency, safety, and energy consumption during TBM operation.

Generally Genius: A Generals.io Agent Development and Data Collection Framework

We present an agent development and data collection framework for Generals.io (GIO)--a real-time strategy game with imperfect information in which players attempt to gain control of opponents' starting positions within a 2D grid world. The framework provides event-based communication amongst several modules implemented as microservices, enabling real-time data collection from GIO's streaming data. Its modular design facilitates rapid bot development and testing, while the emphasis on data collection makes it easy to analyze agent performance. We use this framework in a case study of a top-performing GIO agent called Flobot. Our analysis demonstrates that Flobot's performance varies based on its starting position. Based on the analysis performed with our framework, we propose a modification to Flobot's pathfinding algorithm. Statistical tests show that the new algorithm results in a significant reduction in performance variance.

Regularized Zero-Variance Control Variates

Zero-variance control variates (ZV-CV) are a post-processing method to reduce the variance of Monte Carlo estimators of expectations using the derivatives of the log target. Once the derivatives are available, the only additional computational effort lies in solving a linear regression problem. Significant variance reductions have been achieved with this method in low dimensional examples, but the number of covariates in the regression rapidly increases with the dimension of the target. In this paper, we present compelling empirical evidence that the use of penalized regression techniques in the selection of high-dimensional control variates provides performance gains over the classical least squares method. Another type of regularization based on using subsets of derivatives, or a priori regularization as we refer to it in this paper, is also proposed to reduce computational and storage requirements. Several examples showing the utility and limitations of regularized ZV-CV for Bayesian inference are given. The methods proposed in this paper are accessible through the R package ZVCV.

Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

Abstract Physics-constrained machine learning is emerging as an important topic in the field of machine learning for physics. One of the most significant advantages of incorporating physics constraints into machine learning methods is that the resulting model requires significantly less data to train. By incorporating physical rules into the machine learning formulation itself, the predictions are expected to be physically plausible. Gaussian process (GP) is perhaps one of the most common methods in machine learning for small datasets. In this paper, we investigate the possibility of constraining a GP formulation with monotonicity on three different material datasets, where one experimental and two computational datasets are used. The monotonic GP is compared against the regular GP, where a significant reduction in the posterior variance is observed. The monotonic GP is strictly monotonic in the interpolation regime, but in the extrapolation regime, the monotonic effect starts fading away as one goes beyond the training dataset. Imposing monotonicity on the GP comes at a small accuracy cost, compared to the regular GP. The monotonic GP is perhaps most useful in applications where data are scarce and noisy, and monotonicity is supported by strong physical evidence.

Enhanced recovery after cleft palate repair: A quality improvement project.

Children undergoing cleft palate repair present challenges to postoperative management due to several factors that can complicate recovery. Utilization of multimodal analgesic protocols can improve outcomes in this population. We report experience designing and implementing an enhanced recovery after surgery (ERAS) pathway for cleft palate repair to optimize postoperative recovery. The primary aim was to implement an ERAS pathway with >70% bundle adherence to achieve a 30% reduction in postoperative opioid consumption within 12 months. Our secondary aims assessed intraoperative opioid consumption, length of stay, timeliness of oral intake, and respiratory recovery. A multidisciplinary team of perioperative providers developed an ERAS pathway for cleft palate patients. Key drivers included patient and provider education, formal pathway creation and implementation, multimodal pain therapy, and target-based care. Interventions included maxillary nerve blockade and enhanced intra- and postoperative medication regimens. Outcomes were displayed as statistical process control charts. Pathway compliance was 77.0%. Patients during the intervention period (n=39) experienced a 49% reduction in postoperative opioid consumption (p < .0001) relative to our historical cohort (n=63), with a mean difference of -0.33 ± 0.11 mg/kg (95% CI -0.55 to -0.12 mg/kg). Intraoperative opioid consumption was reduced by 36% (p=.002), with a mean difference of -0.27 ± 0.09 mg/kg (95% CI -0.45 to -0.09 mg/kg). Additionally, patients in the intervention group had a 45% reduction in time to first oral intake (p=.02) relative to our historical cohort, with a mean difference of -3.81 ± 1.56 h (95% CI -6.9 to -0.70). There was no difference in PACU or hospital length of stay, but there was a significant reduction in variance of all secondary outcomes. Opioid reduction and improved timeliness of oral intake is possible with an ERAS protocol for cleft palate repair, but our protocol did not alter PACU or hospital length of stay.

PERFORMANCE OF NUMERICAL WEATHER PRODUCTS FOR INSAR TROPOSPHERIC CORRECTION: A CASE STUDY OF A TROPICAL REGION

Abstract. Tropospheric delay variability remains a significant source of error in the InSAR-derived measurements. Numerical weather models have been proposed as an alternative technique to mitigate tropospheric delays in InSAR and have become a standard procedure for some multi-temporal InSAR processing workflows. This study evaluates the viability of three numerical weather models for mitigating tropospheric delay in InSAR for a tropical region. We assess their performance in correcting tropospheric delay in Sentinel-1 interferograms at different spatial wavelengths using variograms. Their performance is validated using GNSS tropospheric delay and our proposed SAR-derived tropospheric delay estimates. The results indicate that numerical weather model estimates do not mitigate short-wavelength turbulent delays, but can mitigate long-wavelength stratified delays to some extent, which may also introduce additional errors in interferograms. At a spatial wavelength of 40 km, 36% of the interferograms showed increased spatial autocorrelation after correction with GACOS, 55% with ERA-5, and 51% with MERRA-2. In contrast the InSAR-derived tropospheric delays resulted in a significant reduction in variance at all wavelengths indicating the ability to mitigate both turbulent and stratified delays. Our study demonstrates the limited potential of numerical weather model estimates to satisfactorily mitigate trophospheric noise in InSAR and the capability of InSAR-derived trophospheric delay to significantly correct tropospheric noise in InSAR.

Effects of Autonomous Driving Behavior on Intersection Performance and Safety in the Presence of White Phase for Mixed-Autonomy Traffic Stream

This paper studies the effects of different autonomous driving behaviors on an isolated intersection’s safety and mobility performance measures in a mixed-autonomy environment. The movement of vehicles through the intersection is controlled by green, red, and “white” signal indications. Traffic operations during green and red signals are identical to a typical intersection. However, in the presence of the white phase, connected human-driven vehicles (CHVs) should follow connected and autonomous vehicles (CAVs) to pass the intersection safely. Three levels of driving aggressiveness for CAVs are considered: (1) cautious behavior, (2) normal behavior, and (3) aggressive behavior. The mobility and safety impacts of these CAV behaviors are studied based on different CAV market penetration rates and demand levels. The results indicate that a more aggressive CAV driving behavior leads to a lower average delay while increasing the average number of stops for CAVs. Additionally, a more aggressive CAV driving behavior leads to more frequent activation of the white phase that contributes to significant reduction in the speed variance. Moreover, the total number of rear-end near-collision observations with a time to collision of less than 10 s decreases as the CAV penetration rate and aggressiveness level increase. The main reason for this observation is that aggressive CAVs have higher acceleration and lower deceleration values and, therefore, have more flexibility to avoid a crash.

Little data is often enough for distance-based outlier detection

Many real-world use cases benefit from fast training and prediction times, and much research went into speeding up distance-based outlier detection methods to millions of data points. Contrary to popular belief, our findings suggest that little data is often enough for distance-based outlier detection models. We show that using only a tiny fraction of the data to train distance-based outlier detection models often leads to no significant reduction in predictive performance and detection variance over a wide range of tabular datasets. Furthermore, we compare a data reduction based on random subsampling and clustering-based prototypes and show that both approaches yield similar outlier detection results. Simple random subsampling, thus, proves to be a useful benchmark and baseline for future research on speeding up distance-based outlier detection.

Data-driven trajectory prediction with weather uncertainties: A Bayesian deep learning approach

Trajectory prediction is an essential component of the next generation national air transportation system. Reliable trajectory prediction models need to consider uncertainties coming from multiple sources. Environmental factor is one of the most significant reasons affecting trajectory prediction models and is the focus of this study. This paper propose an advanced Bayesian Deep Learning method for aircraft trajectory prediction considering weather impacts. A brief review of both deterministic and probabilistic trajectory prediction methods is given, with a specific focus on learning-based methods. Next, a deterministic trajectory prediction model with classical deep learning methods is proposed to handle both spatial and temporal information using a nested convolution neural network, recurrent neural network, and fully-connected neural network. Following this, the deterministic neural network model is extended to be a Bayesian deep learning model to consider uncertainties where the posterior distributions of parameters are estimated with variational inference for enhanced efficiency. Both mean prediction and confidence intervals are obtained giving the last on-file flight plans and weather data in the region. The proposed methodology is validated using air traffic and weather data from the Sherlock data warehouse. Data pre-processing procedures for big data analytics are discussed in detail. Demonstration and metrics-based validation are performed during severe convective weather conditions for several air traffic control centers. The results show a significant reduction in prediction variance. A comparison with existing methods is also performed. Several conclusions and future works are given based on the proposed study.

Land Cover-Specific Local Incidence Angle Correction: A Method for Time-Series Analysis of Forest Ecosystems

This study deals with a local incidence angle correction method, i.e., the land cover-specific local incidence angle correction (LC-SLIAC), based on the linear relationship between the backscatter values and the local incidence angle (LIA) for a given land cover type in the monitored area. Using the combination of CORINE Land Cover and Hansen et al.’s Global Forest Change databases, a wide range of different LIAs for a specific forest type can be generated for each scene. The algorithm was developed and tested in the cloud-based platform Google Earth Engine (GEE) using Sentinel-1 open access data, Shuttle Radar Topography Mission (SRTM) digital elevation model, and CORINE Land Cover and Hansen et al.’s Global Forest Change databases. The developed method was created primarily for time-series analyses of forests in mountainous areas. LC-SLIAC was tested in 16 study areas over several protected areas in Central Europe. The results after correction by LC-SLIAC showed a reduction of variance and range of backscatter values. Statistically significant reduction in variance (of more than 40%) was achieved in areas with LIA range &gt;50° and LIA interquartile range (IQR) &gt;12°, while in areas with low LIA range and LIA IQR, the decrease in variance was very low and statistically not significant. Six case studies with different LIA ranges were further analyzed in pre- and post-correction time series. Time-series after the correction showed a reduced fluctuation of backscatter values caused by different LIAs in each acquisition path. This reduction was statistically significant (with up to 95% reduction of variance) in areas with a difference in LIA greater than or equal to 27°. LC-SLIAC is freely available on GitHub and GEE, making the method accessible to the wide remote sensing community.

An approach to minimize aircraft motion bias in multi-hole probe wind measurements made by small unmanned aerial systems

Abstract. A multi-hole probe mounted on an aircraft provides the air velocity vector relative to the aircraft, requiring knowledge of the aircraft spatial orientation (e.g., Euler angles), translational velocity and angular velocity to translate this information to an Earth-based reference frame and determine the wind vector. As the relative velocity of the aircraft is typically an order of magnitude higher than the wind velocity, the extracted wind velocity is very sensitive to multiple sources of error including misalignment of the probe and aircraft coordinate system axes, sensor error and misalignment in time of the probe and aircraft orientation measurements in addition to aerodynamic distortion of the velocity field by the aircraft. Here, we present an approach which can be applied after a flight to identify and correct biases which may be introduced into the final wind measurement. The approach was validated using a ground reference, different aircraft and the same aircraft at different times. The results indicate a significant reduction in wind velocity variance at frequencies which correspond to aircraft motion.

Multivariate continuous-time modeling of wind indexes and hedging of wind risk

With the introduction of the exchange-traded German wind power futures, opportunities for German wind power producers to hedge their volumetric risk are present. We propose two continuous-time multivariate models for wind power utilization at different wind sites, and discuss the properties and estimation procedures for the models. Applying the models to wind index data for wind sites in Germany and the underlying wind index of exchange-traded wind power futures contracts, the estimation results of both models suggest that they capture key statistical features of the data. We show how these models can be used to find optimal hedging strategies using exchange-traded wind power futures for the owner of a portfolio of so-called tailor-made wind power futures. Both in-sample and out-of-sample hedging scenarios are considered, and, in both cases, significant variance reductions are achieved. Additionally, the risk premium of the German wind power futures is analysed, leading to an indication of the risk premium of tailor-made wind power futures.

Accelerated Multilevel Monte Carlo With Kernel‐Based Smoothing and Latinized Stratification

AbstractHeterogeneity and a paucity of measurements of key material properties undermine the veracity of quantitative predictions of subsurface flow and transport. For such model forecasts to be useful as a management tool, they must be accompanied by computationally expensive uncertainty quantification, which yields confidence intervals, probability of exceedance, and so forth. We design and implement novel multilevel Monte Carlo (MLMC) algorithms that accelerate estimation of the cumulative distribution functions (CDFs) of quantities of interest, for example, water breakthrough time or oil production rate. Compared to standard non‐smoothed MLMC, the new estimators achieve a significant variance reduction at each discretization level by smoothing the indicator function with a Gaussian kernel or replacing standard Monte Carlo (MC) with the recently developed hierarchical Latinized stratified sampling (HLSS). After validating the kernel‐smoothed MLMC and HLSS‐enhanced MLMC methods on a single‐phase flow test bed, we demonstrate that they are orders of magnitude faster than standard MC for estimating the CDF of breakthrough times in multiphase flow problems.

A bias-variance analysis of state-of-the-art random forest text classifiers

Random forest (RF) classifiers do excel in a variety of automatic classification tasks, such as topic categorization and sentiment analysis. Despite such advantages, RF models have been shown to perform poorly when facing noisy data, commonly found in textual data, for instance. Some RF variants have been proposed to provide better generalization capabilities under such challenging scenario, including lazy, boosted and randomized forests, all which exhibit significant reductions on error rate when compared to the traditional RFs. In this work, we analyze the behavior of such variants under the bias-variance decomposition of error rate. Such an analysis is of utmost importance to uncover the main causes of the observed improvements enjoyed by those variants in classification effectiveness. As we shall see, significant reductions in variance along with stability in bias explain a large portion of the improvements for the lazy and boosted RF variants. Such an analysis also sheds light on new promising directions for further enhancements in RF-based learners, such as the introduction of new randomization sources on both, lazy and boosted variants.

Robustness of prediction for extreme adaptive optics systems under various observing conditions

Context. For high-contrast imaging systems, such as VLT/SPHERE, the performance of the system at small angular separations is contaminated by the wind-driven halo in the science image. This halo is a result of the servo-lag error in the adaptive optics (AO) system due to the finite time between measuring the wavefront phase and applying the phase correction. One approach to mitigating the servo-lag error is predictive control. Aims. We aim to estimate and understand the potential on-sky performance that linear data-driven prediction would provide for VLT/SPHERE under various turbulence conditions. Methods. We used a linear minimum mean square error predictor and applied it to 27 different AO telemetry data sets from VLT/SPHERE taken over many nights under various turbulence conditions. We evaluated the performance of the predictor using residual wavefront phase variance as a performance metric. Results. We show that prediction always results in a reduction in the temporal wavefront phase variance compared to the current VLT/SPHERE AO performance. We find an average improvement factor of 5.1 in phase variance for prediction compared to the VLT/SPHERE residuals. When comparing to an idealised VLT/SPHERE, we find an improvement factor of 2.0. Under our 27 different cases, we find the predictor results in a smaller spread of the residual temporal phase variance. Finally, we show there is no benefit to including spatial information in the predictor in contrast to what might have been expected from the frozen flow hypothesis. A purely temporal predictor is best suited for AO on VLT/SPHERE. Conclusions. Linear prediction leads to a significant reduction in phase variance for VLT/SPHERE under a variety of observing conditions and reduces the servo-lag error. Furthermore, prediction improves the reliability of the AO system performance, making it less sensitive to different conditions.

Abstract TP134: Effects of Strict Anesthesia Management in a Trial of Surgical Revascularization for Intracranial Atherosclerosis

Introduction: Specific aspects of anesthesia management in clinical trials for cerebrovascular diseases have not been systematically addressed. As part of the EDAS Revascularization for Intracranial Atherosclerosis (ERSIAS) trial, we enforced strict management of hemodynamic parameters to prevent cerebral hypoperfusion during surgery. Methods: All patients enrolled in ERSIAS received intensive medical management, including antiplatelet therapy, even the day of surgery. Before every operation, a set of specific goals were discussed with the anesthesia team in a preoperative briefing, including strict regulation of SBP (lower limit = patient’s baseline when asymptomatic - upper limit = 200 mmHg), end-tidal CO 2 (ETCO 2 ) (35-45 mmHg while intubated), and fluid balance (even to positive 2L). Printed goals were posted by the anesthesia stations, anesthesia equipment alarms were set to the predetermined goals, and surgeons had continuous access to the patient’s vitals. Range-deviations lasting more than 5 minutes were recorded. Mannitol and high doses of steroids were avoided. Results: Fifty-two patients underwent EDAS surgery, four had ischemic strokes, and only one patient had perioperative ischemia. There was a significant reduction in the standard deviation variance of intraoperative SBP compared to the SBP during clinic visits (14.9 vs.23.9 mmHg p&lt;0.01), reflecting a tighter SBP control during surgery. SBP goal deviations occurred in five cases, resulting in one perioperative stroke. In general, strokes were more common among patients with SBP goal deviations (20% vs.4.7%). Mean ETCO 2 was 38mmHg (SD=1, Range: 35-41 mmHg). There was only one ETCO 2 goal deviation with no clinical consequences. Fluid balance ranged between -0.25 and 3.1L, with a mean 1.2L (SD=0.6L). Mean estimated blood loss was 37 mL (SD=16, Range: 10-80mL). There were five deviations from the fluid protocol not associated with clinical complications. Conclusion: A goal-oriented pre-surgical briefing with anesthesia team and practical implementations, as discussed above, were effective in reducing hemodynamic variability in the ERSIAS trial. Rigorous SBP management is key in averting stroke during EDAS. Future trials should include standardized anesthesia protocols.

Pricing Asian Options with Stochastic Convenience Yield and Jumps

We price Asian options on commodity futures contracts in the presence of stochastic convenience yield, stochastic interest rates and jumps in the commodity spot price. We obtain a closed-form solution for the case of a geometric average option without the presence of jumps, both for continuous and discrete averaging. This analytic result enables us to employ the geometric average option as suitable control variate for pricing the corresponding arithmetic average Asian option via Monte Carlo simulation. We observe a significant reduction in the size of confidence intervals in relation to plain Monte Carlo. Varying the parameters of the model, we obtain a good understanding as to how Asian option prices change accordingly in relation to a stochastic convenience yield. We then consider a variation of the model by adding stochastic jumps to the commodity spot price dynamics. By conditioning on the jump times first and then averaging over the sequences of jump times, we show that our control variate still provides a significant variance reduction, even though a closed-form solution for a geometric average Asian option in the presence of jumps is unavailable.