One-dimensional Monte Carlo Simulation Research Articles

Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility

Alexander Lipton and Artur Sepp combine the one-dimensional Monte Carlo simulation and the semi-analytical one-dimensional heat potential method to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. The authors� approach to barrier options valuation utilizes two loops. First, the authors run the outer loop by generating volatility paths via the Monte Carlo method. Second, the authors condition the price dynamics on a given volatility path and apply the method of heat potentials to solve the conditional problem in closed form in the inner loop. Lipton and Sepp illustrate the accuracy and efficacy of their semi-analytical approach by comparing it with the two-dimensional Monte Carlo simulation and a hybrid method, which combines the finite-difference technique for the inner loop and the Monte Carlo simulation for the outer loop. The authors apply their method for computation of state probabilities (Green's function), survival probabilities, and values of call options with barriers. The approach provides better accuracy and is orders of magnitude faster than the existing methods. As a by-product of their analysis, Lipton and Sepp generalize Willard's (1997) conditioning formula for valuation of path-independent options to path-dependent options and derive a novel expression for the joint probability density for the value of drifted Brownian motion and its running minimum.

In vivo observation and biophysical interpretation of time-dependent diffusion in human cortical gray matter

The dependence of the diffusion MRI signal on the diffusion time t is a hallmark of tissue microstructure at the scale of the diffusion length. Here we measure the time-dependence of the mean diffusivity D(t) and mean kurtosis K(t) in cortical gray matter and in 25 ​gray matter sub-regions, in 10 healthy subjects. Significant diffusivity and kurtosis time-dependence is observed for t=21.2-100 ​ms, and is characterized by a power-law tail ∼t−ϑ with dynamical exponent ϑ. To interpret our measurements, we systematize the relevant scenarios and mechanisms for diffusion time-dependence in the brain. Using the effective medium theory formalism, we derive an exact relation between the power-law tails in D(t) and K(t). The estimated dynamical exponent ϑ≃1/2 in both D(t) and K(t) is consistent with one-dimensional diffusion in the presence of randomly positioned restrictions along neurites. We analyze the short-range disordered statistics of synapses on axon collaterals in the cortex, and perform one-dimensional Monte Carlo simulations of diffusion restricted by permeable barriers with a similar randomness in their placement, to confirm the ϑ=1/2 exponent. In contrast, the Kärger model of exchange is less consistent with the data since it does not capture the diffusivity time-dependence, and the estimated exchange time from K(t) falls below our measured t-range. Although we cannot exclude exchange as a contributing factor, we argue that structural disorder along neurites is mainly responsible for the observed time-dependence of diffusivity and kurtosis. Our observation and theoretical interpretation of the t−1/2 tail in D(t) and K(t) altogether establish the sensitivity of a macroscopic MRI signal to micrometer-scale structural heterogeneities along neurites in human gray matter in vivo.

Photomechanical Energy Conversion Using Polymer Brush Dissociation

A device is investigated that continuously and directly converts light into mechanical energy, using polymers and photodissociation. A polymer brush tethered to a surface is brought into contact with a parallel plate a small distance above it that contains reaction sites where photodissociation of bound polymer and light can occur. Under the appropriate conditions, the collective effect of these polymers is predicted to apply a force parallel to the plates, converting incoming light into mechanical work. Numerical work is carried out to understand this effect, a three-dimensional Langevin simulation, solution to the Fokker–Planck equation, and a one-dimensional Monte Carlo simulation. Theoretical analysis of the Fokker–Planck equation is used to study a model where equilibration of the unbound state occurs and equilibration to a metastable equilibrium is achieved in the bound state. It is shown that the work per cycle can be made much larger than the thermal energy but at the expense of requiring a greatl...

Distribution of charge carrier transport properties in organic semiconductors with Gaussian disorder

The charge carrier drift mobility in disordered semiconductors is commonly graphically extracted from time-of-flight (TOF) photocurrent transients yielding a single transit time. However, the term transit time is ambiguously defined and fails to deliver a mobility in terms of a statistical average. Here, we introduce an advanced computational procedure to evaluate TOF transients, which allows to extract the whole distribution of transit times and mobilities from the photocurrent transient, instead of a single value. This method, extending the work of Scott et al. (Phys. Rev. B 46, 8603 (1992)), is applicable to disordered systems with a Gaussian density of states and its accuracy is validated using one-dimensional Monte Carlo simulations. We demonstrate the superiority of this new approach by comparing it to the common geometrical analysis of hole TOF transients measured on poly(3-hexyl thiophene-2,5-diyl). The extracted distributions provide access to a very detailed and accurate analysis of the charge carrier transport. For instance, not only the mobility given by the mean transit time but also the mean mobility can be calculated. Whereas the latter determines the macroscopic photocurrent, the former is relevant for an accurate determination of the energetic disorder parameter σ within the Gaussian disorder model. σ derived by using the common geometrical method is, as we show, underestimated instead.

Practical Stochastic Optimal Guidance Law for Bounded Acceleration Missiles

The purpose of this paper is to develop an optimal guidance law that takes into account both the missile acceleration limit and a maximum value allowed for the guidance gain. The maximum value of the guidance gain is dictated mainly by the possible coupling between the missile body motions and the measurement of the inertial target line-of-sight angle rate. The tools for this work are the linear quadratic stochastic Gaussian optimal control theory coupled with the use of random-input describing functions. Although the use of the random-input describing function introduces an approximation in the work, it has been shown in the past that the use of random-input describing functions in miss distance calculations results in good approximations for the predicted miss distance. The paper includes the derivation of the optimal guidance law that accounts for both the missile acceleration limit and the constraint on the guidance gain and a simple one-dimensional Monte Carlo simulation to examine the performance of the guidance law.

Consumer Phase Risk Assessment for Listeria monocytogenes in Deli Meats

The foodborne disease risk associated with the pathogen Listeria monocytogenes has been the subject of recent efforts in quantitative microbial risk assessment. Building upon one of these efforts undertaken jointly by the U.S. Food and Drug Administration and the U.S. Department of Agriculture (USDA), the purpose of this work was to expand on the consumer phase of the risk assessment to focus on handling practices in the home. One-dimensional Monte Carlo simulation was used to model variability in growth and cross-contamination of L. monocytogenes during food storage and preparation of deli meats. Simulations approximated that 0.3% of the servings were contaminated with >10(4) CFU/g of L. monocytogenes at the time of consumption. The estimated mean risk associated with the consumption of deli meats for the intermediate-age population was approximately 7 deaths per 10(11) servings. Food handling in homes increased the estimated mean mortality by 10(6)-fold. Of all the home food-handling practices modeled, inadequate storage, particularly refrigeration temperatures, provided the greatest contribution to increased risk. The impact of cross-contamination in the home was considerably less. Adherence to USDA Food Safety and Inspection Service recommendations for consumer handling of ready-to-eat foods substantially reduces the risk of listeriosis.

Investigations of Contaminated Fluvial Sediment Deposits: Merging of Statistical and Geomorphic Approaches

Concentrations of contaminants in sediment deposits can have large spatial variability resulting from geomorphic processes acting over long time periods. Thus, systematic (e.g., regularly spaced sample locations) or random sampling approaches might be inefficient and/or lead to highly biased results. We demonstrate the bias associated with systematic sampling and compare these results to those achieved by methods that merge a geomorphic approach to evaluating the physical system and stratified random sampling concepts. By combining these approaches, we achieve a more efficient and less biased characterization of sediment contamination in fluvial systems. These methods are applied using a phased sampling approach to characterize radiological contamination in sediment deposits in two semiarid canyons that have received historical releases from the Los Alamos National Laboratory. Uncertainty in contaminant inventory was used as a metric to evaluate the adequacy of sampling during these phased investigations. Simple, one-dimensional Monte Carlo simulations were used to estimate uncertainty in contaminant inventory. We also show how one can use stratified random sampling theory to help estimate uncertainty in mean contaminant concentrations.

Anomalous viscosity exponent in a discretized model for a chain diffusion in one dimension

We present a one-dimensional Monte Carlo simulation for the diffusion motion of a chain of N beads. We found that the scaling exponent for the viscosity can be smaller or greater than 3. This anomalous behavior cannot be attributed to the diffusivity scaling or the length fluctuations but is due to the chain dynamics details during diffusion in which the end beads play the key role. The viscosity exponent 3 and its expected relation with the diffusivity exponent are recovered in the asymptotic regime (N ↦∞).

A risk assessment for methylmercury in tuna

An analysis of the risk of a developmental delay or neurological impairment in children as a result of exposure to MeHg from tuna consumption was conducted. Data used as a basis for the analyses were obtained from surveys of tuna intake, MeHg concentrations in tuna, MeHg levels in the blood of pregnant women, individual relationships between dietary intake and blood levels, individual relationships between blood levels and hair levels, and individual relationships between hair levels and indices of behavioral and neurological performance. Causal or associational relationships, population variability, and uncertainty were modeled for the six data sets. Two predictive models were constructed using the model components. The first was designed to predict the risk of a delay in the onset of talking in a child of a mother who frequently consumes tuna (90 g-day-1). This model uses a one-dimensional Monte-Carlo simulation to assimilate the uncertainties. An average delay of 3-4 days was est imated. The second model was designed to compare the impact of several regulatory options on the risk among the population of tuna-eaters using a scale of central nervous system dysfunction expressly constructed for the assessment. A two-dimensional Monte-Carlo simulation was used to assimilate the distributional components describing population variability and uncertainty.

Three-dimensional Monte Carlo calculation of the VUV electroluminescence and other electron transport parameters in xenon

The paper presents a set of electroluminescence and other transport parameters calculated using a detailed three-dimensional Monte Carlo method, which simulates the drift of electrons in gaseous xenon (p=760 Torr, T=293 K) under reduced electric fields E/N in the 3 to 16 Td range (E/P approximately 1 to 5 V cm-1 Torr-1), which is the region for secondary scintillation production in xenon filled gas proportional scintillation counters. Results are compared with available experimental or theoretical data as well as an earlier one-dimensional Monte Carlo simulation. The calculated parameters are the excitation and scintillation efficiencies and the reduced light yield, together with mean time intervals, mean drift distances and mean number of elastic collisions between xenon excitation collisions. The authors also present electron drift velocities, mobilities and characteristic energies, as well as mean electron energy and electron energy distribution functions.

Stochastic analysis of unsaturated flow: One‐dimensional Monte Carlo simulations and comparisons with spectral perturbation analysis and field observations

A numerical experiment was designed to study the stochastic behavior of one‐dimensional transient unsaturated flow in a Monte Carlo setting. Soil hydraulic properties, log‐saturated hydraulic conductivity ln Ks, pore size distribution parameter α, and the specific water capacity C are assumed to be statistically homogeneous random fields described by exponential correlation functions with identical correlation lengths. Fifty realizations of each soil hydraulic property, with statistical properties obtained from a field experiment, are generated by using a nearest‐neighbor model. Numerical solutions of the one‐dimensional flow equation are used repeatedly to obtain realizations of soil water pressure head ψ and flux q corresponding to the realizations of In Ks, α, and C. The dependence of ψ and q on the statistical properties of ln Ks, α, and C and the magnitude of the hydraulic head gradient G prevailing at the lower boundary are investigated. In addition, results of Monte Carlo analysis and spectral perturbation analyses are compared with field observations. The greatest variability of ψ and q are observed when soil hydraulic properties are uncorrelated and have large variances and integral scales and when G at the lower boundary is unity. The Monte Carlo and spectral perturbation analyses tend to agree reasonably well for the flow domains in which ergodicity of local soil hydraulic properties is assured. Results of the Monte Carlo and spectral perturbation analyses are also supported by field observations.

Stochastic analysis of unsaturated flow: One-dimensional Monte Carlo simulations and comparisons with spectral perturbation analysis and field observations

Stochastic analysis of unsaturated flow: One-dimensional Monte Carlo simulations and comparisons with spectral perturbation analysis and field observations

Stochastic model of staging in graphite intercalation compounds

A stochastic model is presented for staging transitions in graphite intercalation compounds. Three types of kinetic processes are introduced into the domain model of Daumas and Herold, and a one-dimensional Monte Carlo simulation is carried out within the framework of a single-column model to study the time evolution of the system for a variety of cases of staging transitions. Results of Monte Carlo simulations from stage 3 to stage 2 after a sudden change of chemical potential show that the staging transition depends sensitively on the final value of the chemical potential μf, temperature of the system, and the kinetic coefficients. When μf is taken in a certain range in the phase diagram, the time evolution of the structure factor demonstrates the coexistence and no significant broadening of peaks corresponding to the initial and final stage states. For other values of μf, it is observed that the staging transitions proceed via disordered states and in some cases the final states are also disordered. Similar results are obtained for staging transitions from stage 4 to stage 3. Simulations are also made for staging transitions in which the start is from stage 4 and suddenly μ changes to a value in the stage-2 stable region. It is found that the system transforms either directly into a stage-2 state or into a metastable stage-3 state without showing evidence of further transition into a final stage-2 state, depending upon the values of μf, and kinetic coefficients. A discussion is presented on the possibility of observing an intermediate metastable stage-3 state during the transition from stage 4 to stage 2.

Advantages of Collocation Methods Over Finite Differences in One-Dimensional Monte Carlo Simulations of Submicron Devices

Collocation methods are very useful when one-dimensional Monte Carlo simulations of semiconductor submicron devices require a very accurate solution of Poisson's equation. Potential and electric field may be solved simultaneously with better accuracy than using finite differences. The extension to two dimensions is also outlined. We present the results obtained for Monte Carlo simulation of submicron W/Si and AuGaAs Schottky barrier diodes under forward bias conditions. The accurate solution for the electric field at the ohmic contact boundary allows us to model the injected current and to account for depletion of carriers. Tunnelling effects across the barrier are also included in the simulation.

Advantages of collocation methods over finite differences in one-dimensional Monte Carlo simulations of submicron devices

Collocation methods are very useful when one-dimensional Monte Carlo simulations of semiconductor submicron devices require a very accurate solution of Poisson's equation. Potential and electric field may be solved simultaneously with better accuracy than using finite differences. The extension to two dimensions is also outlined. We present the results obtained for Monte Carlo simulation of submicron W/Si and AuGaAs Schottky barrier diodes under forward bias conditions. The accurate solution for the electric field at the ohmic contact boundary allows us to model the injected current and to account for depletion of carriers. Tunnelling effects across the barrier are also included in the simulation.

Monte Carlo simulation of AlGaAs/GaAs heterojunction bipolar transistors

A first demonstration of one-dimensional Monte Carlo simulations of AlGaAs/GaAs heterojunction bipolar transistors is reported. The electron motion is solved by a particle model, while the hole motion is solved by a conventional hydrodynamic model. It is shown that the compositional grading of Al x Ga 1-x As in the base region is effective to cause the ballistic acceleration of electrons in the base region, resulting in a high collector current density of above 1 mA/µm2. The current-gain cutoff frequency fT reaches 150 GHz if the size of a transistor is properly designed. Also shown is the relation between the device performances and the electron dynamics investigated.