Analytic results and weighted Monte Carlo simulations for CDO pricing

We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically ∼ 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulas are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.     

Monte Carlo Transition Dynamics and Variance Reduction

For Metropolis Monte Carlo simulations in statistical physics, efficient, easy- to-implement, and unbiased statistical estimators of thermodynamic properties are based on the transition dynamics. Using an Ising model example, we demonstrate (problem-specific) variance reductions compared to conventional histogram estimators. A proof of variance reduction in a microstate limit is presented.     

蒙特卡罗粒子输运问题的全局降方差方法

精确获得中子通量的时间-空间-能量精细分布对于一类非定常粒子输运蒙特卡罗模拟至关重要.以零方差理论为基础,采取化整为零的策略,把蒙特卡罗方法与离散纵标方法相耦合,用近似重要函数指导蒙特卡罗模拟,给出一种实现蒙特卡罗全局降方差的计算方案.数值算例表明,该计算方案获得了全局降方差的效果.     

电子加速器屏蔽室空间散射的蒙特卡罗计算

为解决电子直线加速器屏蔽室的空间散射计算相关问题,采用蒙特卡罗程序MCNP4B进行模拟,使用分步计算的方法,结合分裂和轮盘赌技巧,计算出9MeV驻波直线加速器运行时的空间散射剂量率大小.并实际测量了加速器运行时屏蔽室周围距地面上方1m处的空间散射剂量分布.将计算得到的结果、计算空间散射的经验公式结果和实际测量的结果三者进行了比较分析.结果表明:蒙特卡罗方法计算值比较符合实际测量值,经验公式计算值则存在一定的偏差.     

Forward Monte Carlo computations of fully polarized microwave radiation in non-isotropic media

A completely forward Monte Carlo radiative transfer code has been developed with biasing techniques to efficiently solve the polarized radiative transfer equation for the full Stokes vector. The code has been adapted to accommodate plane parallel/3-D vertically/horizontally inhomogeneous scattering atmospheres in Cartesian geometries. Particular attention has been paid in stochastically treating the propagation, the emission and the scattering through anisotropic media particularly suited for clouds containing perfectly or partially oriented particles. Our modelling is very appealing because all its biasing techniques do not introduce unphysical Stokes vector. Numerical results and comparisons with benchmark tests are presented for verification.     

Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems

We apply the multicanonical Monte Carlo (MMC) method to compute the probability distribution of the received voltage in a chirped return-to-zero system. When computing the probabilities of very rare events, the MMC technique greatly enhances the efficiency of Monte Carlo simulations by biasing the noise realizations. Our results agree with the covariance matrix method over 20 orders of magnitude. The MMC method can be regarded as iterative importance sampling that automatically converges toward the optimal bias so that it requires less a priori knowledge of the simulated system than importance sampling requires. A second advantage is that the merging of different regions of a probability distribution function to obtain the entire function is not necessary in many cases.     

Monte Carlo Methods for Rough Free Energy Landscapes: Population Annealing and Parallel Tempering

Parallel tempering and population annealing are both effective methods for simulating equilibrium systems with rough free energy landscapes. Parallel tempering, also known as replica exchange Monte Carlo, is a Markov chain Monte Carlo method while population annealing is a sequential Monte Carlo method. Both methods overcome the exponential slowing associated with high free energy barriers. The convergence properties and efficiencies of the two methods are compared. For large systems, population annealing is closer to equilibrium than parallel tempering for short simulations. However, with respect to the amount of computation, parallel tempering converges exponentially while population annealing converges only inversely. As a result, for sufficiently long simulations parallel tempering approaches equilibrium more quickly than population annealing.     

Nonlinear phenomenology from quantum mechanics: soliton in a lattice

We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the measurements of the numbers of the atoms at the lattice sites. In particular, importance sampling in the quantum Monte Carlo method arguably produces faithful simulations of individual experiments. Even though the quantum state is invariant under lattice translations, an experiment may show a noisy version of the localized classical soliton.     

热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

Application of the program LISE to fusion-evaporation

A new fusion-evaporation model LisFus for fast calculation of fusion residue cross sections has been developed in the framework of the code LISE. This model can calculate very small cross sections quickly compared to programs using the Monte Carlo method. Such type of the fast calculations is necessary to estimate fusion residue yields. Using this model, the program LISE now has the possibility of calculating the transmission of fusion residues through a fragment separator. It is also possible to use fusion residue cross sections calculated by the program PACE, which has been incorporated in the LISE package. The code PACE is a modified version of JULIAN—the Hillman-Eyal evaporation code using a Monte Carlo code coupling angular momentum. A comparison between PACE and the LisFus model is presented.     

Evading the sign problem in random matrix simulations

We show how the sign problem occurring in dynamical simulations of random matrices at a nonzero chemical potential can be avoided by judiciously combining matrices into subsets. For each subset the sum of fermionic determinants is real and positive such that importance sampling can be used in Monte Carlo simulations. The number of matrices per subset is proportional to the matrix dimension. We measure the chiral condensate and observe that the statistical error is independent of the chemical potential and grows linearly with the matrix dimension, which contrasts strongly with its exponential growth in reweighting methods.     

Effects of random subject rotation on optimised diffusion gradient sampling schemes in diffusion tensor MRI

The choice of the number (N) and orientation of diffusion sampling gradients required to measure accurately the water diffusion tensor remains contentious. Monte Carlo studies have suggested that between 20 and 30 uniformly distributed sampling orientations are required to provide robust estimates of water diffusions parameters. These simulations have not, however, taken into account what effect random subject motion, specifically rotation, might have on optimised gradient schemes, a problem which is especially relevant to clinical diffusion tensor MRI (DT-MRI). Here this question is investigated using Monte Carlo simulations of icosahedral sampling schemes and in vivo data. These polyhedra-based schemes, which have the advantage that large N can be created from optimised subsets of smaller N, appear to be ideal for the study of restless subjects since if scanning needs to be prematurely terminated it should be possible to identify a subset of images that have been acquired with a near optimised sampling scheme. The simulations and in vivo data show that as N increases, the rotational variance of fractional anisotropy (FA) estimates becomes progressively less dependent on the magnitude of subject rotation (), while higher FA values are progressively underestimated as increases. These data indicate that for large subject rotations the B-matrix should be recalculated to provide accurate diffusion anisotropy information.     

Hellman-Feynman operator sampling in diffusion Monte Carlo calculations

Diffusion Monte Carlo (DMC) calculations typically yield highly accurate results in solid-state and quantum-chemical calculations. However, operators that do not commute with the Hamiltonian are at best sampled correctly up to second order in the error of the underlying trial wave function once simple corrections have been applied. This error is of the same order as that for the energy in variational calculations. Operators that suffer from these problems include potential energies and the density. This Letter presents a new method, based on the Hellman-Feynman theorem, for the correct DMC sampling of all operators diagonal in real space. Our method is easy to implement in any standard DMC code.     

Reduced-order modeling of time-dependent reflectance profiles from purely scattering media

Due to the widespread existence and importance of foam, inverse techniques for characterizing industrial foams are of interest. An essential element in an inverse method used to characterize a foam layer is a model of the time-dependent reflectance of a laser pulse. Monte Carlo methods may be used to accurately model reflectance, but these methods are computationally expensive. Computationally efficient methods based on the diffusion approximation have been developed, but this approach is not sufficiently accurate in many cases of interest. Therefore, a computationally efficient and robust method is desirable. This paper presents a computationally efficient method for modeling the time-dependent reflectance of a laser pulse from a non-absorbing, scattering plane layer that is based on reduced-order modeling techniques. The accuracy of the proposed method is demonstrated by comparing reflectance profiles for randomly selected foam layer properties with corresponding profiles that were generated from Monte Carlo simulations.     

DYNAMIC STIFFNESS METHOD FOR CIRCULAR STOCHASTIC TIMOSHENKO BEAMS: RESPONSE VARIABILITY AND RELIABILITY ANALYSES

The problem of characterizing response variability and assessing reliability of vibrating skeletal structures made up of randomly inhomogeneous, curved/straight Timoshenko beams is considered. The excitation is taken to be random in nature. A frequency-domain stochastic finite element method is developed in terms of dynamic stiffness coefficients of the constituent stochastic beam elements. The displacement fields are discretized by using frequency- and damping-dependent shape functions. Questions related to discretizing the inherently non-Gaussian random fields that characterize beam elastic, mass and damping properties are considered. Analytical methods, combined analytical and simulation-based methods, direct Monte Carlo simulations and simulation procedures that employ importance sampling strategies are brought to bear on analyzing dynamic response variability and assessment of reliability. Satisfactory performance of approximate solution procedures outlined in the study is demonstrated using limited Monte Carlo simulations.     

A stochastic model and a variance-reduction Monte-Carlo method for the calculation of light transport

We compare the transport theoretic and a stochastic approach of modeling light propagation in the atmosphere. Computations of LIDAR return signals using algorithms based on the two different approaches show very good agreement of the numerical data. Furthermore, a deeper analysis of the formulas for the LIDAR return signal obtained from two kinds of modeling shows that they are equivalent. Combining these approaches and introducing splitting techniques, variance reduction Monte Carlo methods and codes are designed which are adapted to the configuration of the LIDAR. These codes allow the calculation of multiple scattering effects with high accuracy. Finally, we point out the importance and some perspectives of ultilization of multiple scattering in laser remote sensing of clouds.     

多群伴随中子通量积分方程的一种Monte Carlo新解法

伴随Monte Carlo方法对计算点通量、辐射环境问题等有其独特的优越性,迄今为止是别的方法所不具备的,但伴随Monte Carlo方法所给出的估计的方差常常是比较大的。本文对多群伴随通量积分方程给出一种降低方差的Monte Carlo解法——"最佳"权重变化因子法。计算结果表明,这种方法可使方差明显减小。     

Accurate, efficient, and simple forces computed with quantum Monte Carlo methods

Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We introduce a simple procedure, based on known properties of physical electronic densities, to make the variance of the Hellmann-Feynman estimator finite. We obtain very accurate geometries for the molecules H(2), LiH, CH(4), NH(3), H(2)O, and HF, with a Slater-Jastrow trial wave function. Harmonic frequencies for diatomics are also in good agreement with experiment. An antithetical sampling method is also discussed for additional reduction of the variance.     

蒙特卡罗粒子输运软件JMCT抽样工具库设计

为通用型蒙特卡罗粒子输运程序JMCT设计了抽样工具库,通过两种技术途径提供各分布的抽样。一是针对各种常见分布提供特定抽样子程序;二是提供一个通用型的抽样子程序,可以实现任意离散分布和任意一维有限区间上连续分布的自动抽样。在设计任意一维有限区间上连续分布的自动抽样工具时利用了部分开源代码,利用其功能提供给用户最大的方便性。对抽样工具库的检验表明,其可以正确、方便地实现各种输运模拟中常见分布的抽样。     

Monte Carlo sampling for gamma and beta detectors using a general purpose PC program

The main objective of this study is the computation of several parameters involved in gamma and beta environmental radiation measurements, such as detection efficiency, the attenuation coefficients, mass energy-transfer coefficients and mass energy-absorption coefficients for several materials. In order to accomplish these tasks we developed a PC program, based on a Monte Carlo simulation of radiation transport. This program (GES_MC Gamma-electron Efficiency Simulator) was written entirely in Java and was based on the EGSnrc (Electron Gamma Shower) source code. Although GES_MC was especially designed for the computation of the response function and peak efficiency for gamma detectors, it can also be used in various studies concerning photon or electron interactions with the matter in any cylindrical (RZ) geometry. Several aspects of photon and electron transport and the comparison of the program outputs with experimental data are also presented in this study.The main advantage of the Monte Carlo simulations presented in this paper is that any source and any detector can be properly sampled. In contrast with the Monte Carlo technique, for an accurate experimental result, the computation of detector efficiency for a large number of standard sources having various geometries and compositions is required (one standard source for each sample type).