Monte Carlo Simulations Research Articles

A local volatility correction to mean-reverting stochastic volatility model for pricing derivatives

Generally, in the real market, empirical findings suggest that either local volatility (LV) or stochastic volatility (SV) models have a limit to capture the full dynamics and geometry of the implied volatilities of the given equity options. In this study, to overcome the disadvantage of such LV and SV models, we propose a special type of hybrid stochastic-local volatility (SLV∗) model in which the volatility is given by the squared logarithmic function of the underlying asset price added to a function of a fast mean-reverting process. By making use of asymptotic analysis and Mellin transform, we derive analytic pricing formulas for European derivatives with both smooth and non-smooth payoffs under the SLV∗ model. We run numerical experiments to verify the accuracy of the pricing formulas using a Monte-Carlo simulation method and to display that the proposed new model fits the geometry of the market implied volatility more closely than other models such as the Heston model, the stochastic elasticity of variance (SEV) model, the hybrid stochastic and CEV type local volatility (SVCEV) model and the multiscale stochastic volatility (MSV) model, especially for short time-to-maturity options.

Effectiveness of regional risk mitigation policies in equitably improving connectivity to essential service during hurricane-induced floods

This study aimed to evaluate the effectiveness of regional disaster mitigation policies in providing equitable access to essential services during hurricane-induced floods in Southeast Louisiana. Studies have been conducted on access to essential service facilities during and after disasters. However, there is limited research on whether current regional disaster mitigation plans ensure equitable access to emergency facilities. To this end, a methodology was developed to assess the effect of the 2017 Louisiana Coastal Master Plan developed by the Coastal Protection and Restoration Agency (CPRA) on equity in connectivity to essential service facilities (hospitals and fire stations) in a case study region in southeastern Louisiana. First, a graph-based model was used to represent the road network and determine the connectivity of five demographic groups during hurricane-induced flood scenarios. Herein, a hurricane-induced flood scenario with a low return period (50 years) was chosen for future years up to 2065, considering sea level rise and subsidence. Roads with flood depths exceeding 30 cm were considered impassable and were removed from the network. Connectivity was then determined using breadth-first search. Monte Carlo simulations were performed to propagate uncertainties in flood depths. It was found that minority groups were at a higher risk of losing access to emergency services during the selected hazard scenario. Native American and Asian populations were found to be at the highest risk of disconnection, followed by the Hispanic and African-American populations. Overall, the coastal master plan did not affect the equity (or lack thereof) in connectivity to essential service facilities.

Analyzing neutron and gamma ray shielding properties in varied W-B2O3 ratios: methodological comparisons and Monte Carlo simulation

This study aims to comprehensively assess the radiation shielding efficacy of W-B2O3 composite material across varying ratios, contrasting its performance with glass and established literature data. The investigation involves comparing the radiation shielding capabilities of these materials using Geant4-based GATE simulation, XCOM, and EpiXS programs across energy levels ranging from 0.3–2.516 MeV. The research involved calculating and comparing the effective removal cross-section values of these materials with those commonly employed in neutron shielding. The findings indicate superior radiation shielding capabilities in the composite material compared to glass. Moreover, the mass attenuation coefficients were derived through GATE simulation at energy levels of 6 and 18 MV mono and spectrum energy. These values were then compared with theoretical methods; XCOM, XMuDat, and an innovative methodology outlined in the current literature. In the new approach, the effective atomic numbers of the materials were determined using the mass attenuation coefficients.

Integrating historical storm surge events into flood risk security in the Copenhagen region

Rapid urbanisation along the coasts of the world in recent decades has increased their vulnerability to storm surges, especially in response to mean sea level rise. The unique geographical and social conditions of Copenhagen, a major European coastal city, have prompted urban expansion along Køge Bay to the south of the city. However, this new urbanisation area is confronted with the common obstacle of developing a coastal defence strategy, i.e., the lack of long-term observational data required to determine a reliable storm surge protection level. This study aims to address this issue by developing a framework that integrates historical records of extreme storm surge events into coastal defence strategies, using Copenhagen as a case study. We propose a four-step work framework, including (1) Data collection and analysis: We collected and analysed data from neighbouring cities and used modelling and reanalysis data sets. By combining these sources, we aim to reconstruct historical time series for the study site dating back to 1836. This extended information set enhances our understanding of past storm surge events. (2) Statistical modelling and forecasting: Using Bayesian statistical methods, we fitted the historical storm surge data to appropriate probability distributions. This enabled us to generate probabilistic forecasts of storm surge magnitudes, providing insight into the likelihood of future events and their potential impacts on the coastal area. (3) Sensitivity analyses: We performed sensitivity experiments using Markov chain Monte Carlo (MCMC) methods to identify the most influential parameters, such as thresholds, that affect storm surge levels. This analysis improved our understanding of the key drivers of storm surge events and their uncertainties, further informing coastal defence strategies. (4) Expert judgement and risk management: Expert judgements are implemented to establish the necessary security level to manage flood risks in the city. This helps to ensure that high-impact, low-probability events are adequately considered in risk management efforts. Following this framework, we can develop a comprehensive understanding of storm surge risks in the urbanised region south of Copenhagen and use historical data to inform coastal defence strategies. This study emphasises the importance of incorporating long-term observational data and expert insights to improve the resilience of coastal cities facing the challenges of urbanisation and climate change.

Reinforcement learning-based multi-impulse rendezvous approach for satellite constellation reconfiguration

This paper presents a satellite constellation orbital reconfiguration method based on the intelligent multi-impulse rendezvous considering the impulse-magnitude limit. This problem is solved by two steps: the single-target rendezvous trajectory optimization and the multi-target rendezvous mission planning. For single target, the multi-impulse rendezvous problem is transformed into a Markov decision process and solved by a reinforcement learning algorithm. The rewards of the critic networks are used as estimation of fuel consumption, while the actions of the actor networks are used as initial values for further optimization. For multiple targets, an efficient Monte-Carlo tree search method is used to realize the global optimal solution of the satellite constellation reconfiguration problem. Finally, the numerical examples show that the proposed method can rapidly optimize the multi-impulse constellation reconfiguration problem.

Identifying a class of Ridge-type estimators in binary logistic regression models

In the analysis of logistic regression models, various biased estimators have been proposed as an alternative to the maximum likelihood estimator (MLE) for estimating model parameters in the presence of multicollinearity. In this study, a new class of biased estimators called Logistic Ridge-type Estimator (LRTE) is proposed by generalizing the existing biased estimators that include two biasing parameters. The performance of the proposed estimator is compared with the other biased estimators in terms of the Matrix Mean Squared Error (MMSE). Two separate Monte Carlo simulation studies are conducted to investigate the performance of the proposed estimator. A numerical example is provided to demonstrate the performance of the proposed biased estimator. The results revealed that LRTE performed better than other existing biased estimators under the conditions investigated in this study.

Weighted penalized m-estimators in robust ridge regression: an application to gasoline consumption data

ABSTRACT The OLS and ridge regression (RR) estimators are adversely affected, when the problem of multicollinearity and y-direction outliers occur together. The robust ridge regression with penalized parameters offers biased estimators with lower variance than OLS and RR. The optimal penalized parameter value is crucial for balancing variance and bias. This study proposes three new weighted robust penalized M-estimators to address both multicollinearity and y-direction outliers. Their performance is evaluated against OLS, RR and existing penalized M-estimators using Monte Carlo simulations based on mean squared error (MSE). The new estimators exhibit lower MSE in the presence of multicollinearity and y-direction outliers. A real data application on gasoline consumption demonstrates the superior performance of the new estimators.

Programmable 2D materials through shape-controlled capillary forces

In recent years, self-assembly has emerged as a powerful tool for fabricating functional materials. Since self-assembly is fundamentally determined by the particle interactions in the system, if we can gain full control over these interactions, it would open the door for creating functional materials by design. In this paper, we exploit capillary interactions between colloidal particles at liquid interfaces to create two-dimensional (2D) materials where particle interactions and self-assembly can be fully programmed using particle shape alone. Specifically, we consider colloidal particles which are polygonal plates with homogeneous surface chemistry and undulating edges as this particle geometry gives us precise and independent control over both short-range hard-core repulsions and longer-range capillary interactions. To illustrate the immense potential provided by our system for programming self-assembly, we use minimum energy calculations and Monte Carlo simulations to show that polygonal plates with different in-plane shapes (hexagons, truncated triangles, triangles, squares) and edge undulations of different multipolar order (hexapolar, octopolar, dodecapolar) can be used to create a rich variety of 2D structures, including hexagonal close-packed, honeycomb, Kagome, and quasicrystal lattices. Since the required particle shapes can be readily fabricated experimentally, we can use our colloidal system to control the entire process chain for materials design, from initial design and fabrication of the building blocks, to final assembly of the emergent 2D material.

Imbalances in Two-Level Hierarchical Linear Modeling of Single-Case Data: A Monte Carlo Simulation Study

Hierarchical linear modeling (HLM) is a promising approach that can be applied to explain variability in intervention effectiveness between participants in single-case experimental design (SCED) research. This approach allows the inclusion of participant characteristics as moderators to account for variability in intervention effectiveness. However, little is known about the performance of HLM for analysis with the inclusion of imbalanced intervention starting points and imbalanced moderators. Therefore, the goal of this study is to empirically evaluate the statistical properties of this model through a large-scale Monte Carlo simulation study under these scenarios. The results indicate that imbalanced intervention starting points have no impact on the statistical properties of estimating intervention effects. On the other hand, imbalanced moderators have an impact on estimating the intervention and moderator. How the conditions of imbalanced moderators influence the performance of two-level HLM depends on how the moderators are coded. Two general conclusions can be made. The model results in more favorable statistical properties when (i) a larger number of participants are included and (ii) the variability in continuous moderators is larger. Practical implications for the design and analysis of SCEDs are discussed.

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

Evaluation and prediction of bending properties of glulam beams made from young plantation-grown Eucalyptus nitens

ABSTRACT Interest in making glulam from plantation-grown Eucalyptus nitens has increased, but current structural timber standards were not designed for species grown in plantations. Additionally, the applicability of classical composite beam theory remains uncertain due to the unique features of this species. This study was designed to assess the hypothesis that the bending performance of glulam made from young plantation-grown E. nitens is reliable and predictable. We tested the hypothesis through experimental procedures and theoretical and statistical analyses. First, we assessed the bending performance of 20 glulam beams, which were manufactured in five configurations. Second, we compared our experimental results with predictive values to evaluate the accuracy of methods in current standards. Third, in our pursuit of improved predictive tools, we developed theoretical and parametric models using mechanical properties of the board elements. Our improved models showed a decreased deviation in both stiffness and strength values. A Monte Carlo simulation was used to determine the distribution for both stiffness and strength. The results validated that this product can be allocated a GL grade using current standards and the bending performance is predictable. The study enhances confidence in incorporating E. nitens into glulam products and offers valuable data for future specification modifications.

Frequency Bias Causes Overestimation of Climate Change Impacts on Global Flood Occurrence

AbstractThe frequency change of 100‐year flood events is often determined by fitting extreme value distributions to annual maximum discharge from a historical base period. This study demonstrates that this approach may significantly bias the computed flood frequency change. An idealized experiment shows frequency bias exceeding 100% for a 50‐year base period. Further analyses using Monte Carlo simulations, mathematical derivations, and hydrological model outputs reveal that bias magnitude inversely relates to base period length and is weakly influenced by the generalized extreme value distribution's shape parameter. The bias, persisting across different estimation methods, implies floods may exceed local defenses designed based on short historical records more often than expected, even without climate change. We introduce a frequency bias adjustment method, which significantly reduces the projected rise in global flood occurrence. This suggests a substantial part of the earlier projected increase in flood occurrence and impacts is not attributable to climate change.

Simulation of Neutron Multiplicity Counting Based on Monte Carlo Code RMC

Neutron multiplicity pertains to the probability distribution of the quantity of neutrons released during induced or spontaneous fission processes within fissile materials. The technology for neutron multiplicity measurement leverages temporal correlations in the emission of fission neutrons from nuclear materials. It employs mathematical tools to elucidate the processes of neutron generation, multiplication within the nuclear material, and detection of outside nuclear materials. In this paper, two multiplicity counting methods are devised building on the RMC (Reactor Monte Carlo) code. The results obtained from both methods, including singles, doubles, and triples counting rates, exhibit good agreement with MCNP. Additionally, parameters associated with the detection efficiency and decay time of the apparatus are computed. By amalgamating the acquired singles, doubles, and triples counting rates, the mass of fissile material within the sample is inversely determined using a passive method with the point model equation. Notably, the point model equation reveals that spontaneous fission neutrons and induced neutrons possess distinct energy spectra, challenging the validity of the assumption that the probability of neutrons being captured without causing fission can be disregarded. In light of these considerations, the neutron multiplicity counting equation was rederived. The accuracy of the Monte Carlo simulation results is improved using the new method.

Killing Two Birds with One Stone: Accounting for Unfolding Item Response Process and Response Styles Using Unfolding Item Response Tree Models

Two research streams on responses to Likert-type items have been developing in parallel: (a) unfolding models and (b) individual response styles (RSs). To accurately understand Likert-type item responding, it is vital to parse unfolding responses from RSs. Therefore, we propose the Unfolding Item Response Tree (UIRTree) model. First, we conducted a Monte Carlo simulation study to examine the performance of the UIRTree model compared to three other models – Samejima’s Graded Response Model, Generalized Graded Unfolding Model, and Dominance Item Response Tree model, for Likert-type responses. Results showed that when data followed an unfolding response process and contained RSs, AIC was able to select the UIRTree model, while BIC was biased toward the DIRTree model in many conditions. In addition, model parameters in the UIRTree model could be accurately recovered under realistic conditions, and mis-specifying item response process or wrongly ignoring RSs was detrimental to the estimation of key parameters. Then, we used datasets from empirical studies to show that the UIRTree model could fit personality datasets well and produced more reasonable parameter estimates compared to competing models. A strong presence of RS(s) was also revealed by the UIRTree model. Finally, we provided examples with R code for UIRTree model estimation to facilitate the modeling of responses to Likert-type items in future studies.

Evaluation of acrylamide concentration in commercial falafel available in Tehran City by different cooking methods: A health risk assessment study

The objective of current research was to measure the amount of acrylamide in falafel samples by GC–MS (Gas chromatography–mass spectrometry) technique. The results presented, the average amount of acrylamide in falafel samples was 1.23 ± 0.83 mg/kg (ranged from 0.12 to 3.75 mg/kg). Also, the results showed lower temperature and frying with electric oven and low oil, reduces the average formation of acrylamide (0.73 ± 0.42 mg/kg), while frying at high temperature and frying with gas and immersion in edible oil, increases the average amount of acrylamide formation (1.72 ± 0.86 mg/kg). The highest and lowest average amount of acrylamide was observed in falafel cooked with canola oil (1.57 ± 0.96 mg/kg) and cooked with soybean oil (0.92 ± 0.32 mg/kg), respectively. Based on the MCS (Monte Carlo Simulation) results, the THQ (Target Hazard Quotient) and ILCR (Incremental Lifetime Cancer Risk) related to exposure to acrylamide via commercial falafel for adults were 2.72E-2 and 2.77E-5; and for children were 9.69E-2 and 9.25E-5, respectively. Therefore, there doesn't a significant health risk from falafel consumption.

Effects of growth rate and dynamic substrate tilt on properties of Au-Ta alloy films deposited by high-power impulse magnetron sputtering

Gold‑tantalum (AuTa) alloys are promising for next-generation hohlraums for magnetically-assisted indirect-drive inertial confinement fusion. Hohlraum fabrication involves sputter deposition of ultrathick coatings on sphero-cylindrical substrates. The control of physical properties of such coatings remains a challenge. Here, we systematically study effects of the growth rate and dynamic substrate tilt on properties of AuTa4 films deposited onto rotating planar substrates mounted at different tilt angles to mimic different regions of the sphero-cylindrical surface of a hohlraum. We use high-power impulse magnetron sputtering (HiPIMS) in the constant charge per pulse mode with a pulse duration of 100 μs, a charge per pulse of 190 μC, a peak target current of about 3 A, and the pulse frequency varied in the range of 400–1400 Hz. The Langmuir probe, mass-resolved ion energy spectrometry, and optical emission spectroscopy are used to monitor plasma discharge characteristics in order to isolate and study effects of the growth rate. The deposition rate and the ballistics and energetics of depositing species are estimated by Monte Carlo simulations. Results show that the film microstructure, crystallographic phase, residual stress, and electrical resistivity strongly depend on both the deposition rate and substrate tilt, highlighting their critical role in tailoring properties of AuTa films during hohlraum fabrication.

Fast uncertainty assessment of in-service thrust control for turbofan engines: An equivalent model using Taylor expansion

An equivalent model using Taylor expansion (TEEM) is proposed for a fleet of engines regulated by the industrial baseline controller, aiming at the fast assessment of in-service thrust control under gas path and measurement uncertainties in advance. TEEM is fulfilled initially by the equivalent transformation of measurement uncertainties into engine set-point distribution, followed by a first-order Taylor expansion on the steady-state aero-thermal engine model along the average degradation curve of engine fleets. Simulations are conducted at take-off states on a validated aero-thermal turbofan engine model with publicly available uncertainty statistics on a desktop computer. Results show that the equivalent transformation is successful for both new and degraded engine fleets. Moreover, TEEM can estimate the mean and standard deviation values of key engine control parameters including thrust with the maximum errors of 0.04 % and 3.85 % for new engine fleets, 0.04 % and 6.25 % for degraded engine fleets, respectively, compared to the classic sample-based Monte-Carlo simulations (MCS). Computational time for TEEM and MCS for the tested life cycle are 3,018,564s and 137.52s accordingly, which means 99.995 % simulation time reduction is achieved by TEEM. Hence, the accuracy and efficiency of the proposed model for uncertainty assessment of thrust control of turbofan engines are confirmed.

Modeling the 2014-2015 Vesicular Stomatitis Outbreak in the United States Using an SEIR-SEI Approach.

Vesicular stomatitis (VS) is a vector-borne livestock disease caused by the vesicular stomatitis New Jersey virus (VSNJV). This study presents the first application of an SEIR-SEI compartmental model to analyze VSNJV transmission dynamics. Focusing on the 2014-2015 outbreak in the United States, the model integrates vertebrate hosts and insect vector demographics while accounting for heterogeneous competency within the populations and observation bias in documented disease cases. Key epidemiological parameters were estimated using Bayesian inference and Markov chain Monte Carlo (MCMC) methods, including the force of infection, effective reproduction number (Rt), and incubation periods. The model revealed significant underreporting, with only 10-24% of infections documented, 23% of which presented with clinical symptoms. These findings underscore the importance of including competence and imperfect detection in disease models to depict outbreak dynamics and inform effective control strategies accurately. As a baseline model, this SEIR-SEI implementation is intended to serve as a foundation for future refinements and expansions to improve our understanding of VS dynamics. Enhanced surveillance and targeted interventions are recommended to manage future VS outbreaks.

Modular gas-cooled reactor core optimal design and additive manufacturing performance based on SiC matrix dispersed with TRi-structural ISOtropic fuel

High-temperature gas-cooled reactors present significant technical competitiveness in various fields, such as low-carbon electricity, thermal energy, and hydrogen supply. Silicon Carbide (SiC) matrix dispersed with TRi-structural ISOtropic (TRISO) particle fuel is characterized by high-temperature tolerance, radiation resistance, and good neutron economy, which has emerged as a pivotal technological pathway for reactor core design. With the rapid advancement of SiC Additive Manufacturing (AM) technology, there is a substantial increase in core design flexibility, and an innovative gas-cooled reactor design was proposed by Monte Carlo (MC) method in this paper. The Non-uniform Rational B-spline (NURBS), Latin Hypercube Sampling (LHS), second-order polynomial response surface, as well as Genetic Algorithm (GA) were coupled to realize the optimization design for the coolant channel. Besides, a modular fuel design was proposed, and the AM SiC shell was fabricated using Binder Jetting (BJ) technology. Furthermore, the densification of the AM SiC shell and the matrix with SiC powder and SiC microspheres (TRISO simulator) was investigated by Chemical Vapor Infiltration (CVI). Finally, the microscopic morphology analysis and thermal-mechanical performance characterization of the samples were conducted, which demonstrated the technical feasibility and advanced capabilities of the SiC matrix dispersed with TRISO fuel based on AM technology.

Structural integrity assessment of CANDU pressure tubes using Sobol indices for global sensitivity analysis

CANDU11CANDU is a registered trademark of Atomic Energy of Canada Limited. reactors are a channel-type design where up to 480 zirconium alloy pressure tubes (PTs) act as the reactor pressure boundary. Fitness-for-service standards such as CSA N285.8 (CSA Group, 2015) have been established to prescribe the requirements of pressure tube evaluations to maintain their integrity throughout their lifetime. Probabilistic leak-before-break (LBB) assessments can be used in evaluations to demonstrate that the likelihood of a flaw growing past the stability point while undetected (or before a safe shutdown can be achieved) is below regulatory limits. The assessments typically require a ranking of model parameters based on their influence. The ranking process traditionally uses expert judgment and local sensitivity analysis methods. There has been recent interest in implementing global methods for LBB assessments as they can manage large numbers of variables and extensive sampling spaces. However, their adoption is hindered by the computational cost of the models involved.The current study proposes a method for performing global sensitivity parameter rankings during probabilistic LBB assessments. The study is the continuation of the CANDU nuclear power plant (NPP) pressure tube (PT) case study in El Bouzidi et al., (2024) where a probabilistic approach was implemented in RAVEN (Rabiti and Alfonsi, 2019) to estimate whether the probability of unstable crack growth in PTs is within acceptable limits. This follow-up work proposes surrogate modeling using a high-dimensional model representation to derive Sobol indices and establish a parameter influence ranking. The methodology is demonstrated in a Monte Carlo simulation campaign of a pressure tube inlet rolled joint. The implemented approach successfully identified and quantified critical parameters of the model while efficiently ranking and quantifying the interactions between input variables.