美式期权的Monte Carlo模拟法定价理论及应用

近年来随着计算机技术的飞速发展,美式期权的Monte Carlo模拟法定价取得了实质性的突破。本文分析介绍了美式期权的Monte Carlo模拟法定价理论及在此基础上推导出的线性回归MonteCarlo模拟法定价公式及其在实际的应用。     

DF检验式中漂移项和趋势项的t统计量研究

DF统计量的渐近分布决定于估计的回归中,是否包含一个常数项α或时间趋势δ以及真实随机行走是否有非零漂移项表征,故通常的DF检验过程中包含三种检验式（不含α和δ、只含α、含α和δ）。针对α和δ及其t统计量的分布特征的研究甚少,对它们的极限分布未见有全面的推导,且关于单个回归参数检验统计量的响应面函数目前还无人提供。本文的贡献在于推导了不同检验式中α和δ的t检验统计量的极限分布表达式,并通过蒙特卡罗模拟结果分析了α和δ及其t统计量的分布特征,在此基础上给出有限样本下各检验统计量的响应面函数,从而使得DF检验进一步完善。     

同期相关面板数据退势单位根检验的小样本性质

本文基于SUR回归将时间序列的两种单位根检验（ADF—GLS检验）推广到面板数据,得到了同期相关面板数据退势单位根检验,称为SUR—ADF—GLS检验。通过蒙特卡洛试验研究发现,SUR—ADF—GLS检验具有良好的小样本性质。并且,SUR—ADF—GLS检验关于面板数据的同期相关性结构存在着较强的“依存性”。     

Post-audits for managing cyber security investments: Bayesian post-audit using Markov Chain Monte Carlo (MCMC) simulation

With increasing security spending in organizations, evaluation of the quality and effectiveness of IT security investments has become an important component in managing these projects. The academic literature, however, is largely silent on post-audit of such investments, which is a formal evaluation of IT resource allocation decisions. IT post-audits are considered a useful risk management tool for organizations and are often emphasized in security certifications and standards. To fill this research gap and contribute to practice, we suggest post-auditing of IT security investments using the generic Markov Chain Monte Carlo (MCMC) simulation approach. This approach does not place stringent conjugate assumptions and can handle high-dimensional Bayesian post-audit inference problems often associated with information security resource allocation decisions. We develop two Bayesian post-audit models using the MCMC method: (1) measuring the effectiveness of an IT security investment using posterior mean score ratios (MSR), and posterior crossover error rates (CER); and (2) measuring the effectiveness through detection of a denial of service (DOS) attack using Bayesian estimation to statistically compare the degree of divergence using the concept of entropy. We demonstrate the utility of the proposed methodology using an email intrusion detection system application.     

Finite sample properties for the semiparametric estimation of the intercept of a censored regression model

Financial support for this paper was provided by a C.A. Anderson Fellowship of the Cowles Foundation. I wish to thank Donald Andrews, Moshe Buchinsky, Oliver Linton, and Peter Robinson for helpful discussions. I also wish to thank three anonymous referees for their comments and suggestions. I am, of course, responsible for any remaining errors. A popular two-step estimator of the intercept of a censored regression model is compared with consistent asymptotically normal semiparametric alternatives. Using a root mean squared error criterion, the semiparametric estimators perform better for a range of bandwidth parameter choices for a variety of distributions of the errors and regressors. For error distributions that are close to the normal, however, the two-step parametric estimator performs better.     

Evolutionary game dynamics and distributed recency-weighted learning

This paper presents a relationship between evolutionary game dynamics and distributed recency-weighted Monte Carlo learning. After reviewing some existing theories of replicator dynamics and agent-based Monte Carlo learning, we provide proofs of the formulation-level equivalence between these two models. The relationship will be revealed not only from a theoretical viewpoint, but also by computational simulations of the models. As a consequence, macro dynamic patterns generated by distributed micro-decisions can be explained by parameters defined at an individual level. In particular, given the equivalent formulations, we investigate how the rate of agents’ recency weighting in learning affects the emergent evolutionary game dynamic patterns. An increase in this rate negatively affects the inertia, making the evolutionary stability condition more strict, and positively affecting the evolutionary speed toward equilibrium.JEL Classification: C63, C73Supervisions and advice given by Arthur J. Caplan have greatly contributed to this paper. I am also grateful to the anonymous reviewers for their valuable comments redirecting my presentation to a more appropriate one.     

Nonparametric Bayes inference for concave distribution functions

Bayesian inference for concave distribution functions is investigated. This is made by transforming a mixture of Dirichlet processes on the space of distribution functions to the space of concave distribution functions. We give a method for sampling from the posterior distribution using a Pólya urn scheme in combination with a Markov chain Monte Carlo algorithm. The methods are extended to estimation of concave distribution functions for incompletely observed data.     

A Note on the Prediction Intervals for a Future Ordered Observation from a Pareto Distribution

In the researching of products' reliability, the result of life testing is used as the basis for the evaluation and improvement of reliability. During life testing, however, the future observation in an ordered sample is often expected to be predicted so as to show how long a sample of units might run until all fail in life testing. Therefore, we propose five new pivotal quantities to obtain prediction intervals of future order statistics based on right type II censored samples from the Pareto distribution with known shape parameter, then compares the lengths of the prediction intervals when using the pivotal quantity of Ouyang and Wu (1994) based on best linear unbiased estimator (BLUE) of scale parameter, and these five pivotal quantities. An advantage of these five pivotal quantities is that these are easier to calculate than the pivotal quantity of Ouyang and Wu (1994) based on BLUE of scale parameter, since they need to compute the tables of coefficients of BLUE of scale parameter.     

Bayesian International Evidence on Heavy Tails, Non-Stationarity and Asymmetry over the Business Cycle

Although leptokurtosis is fairly common in macroeconomic time series, agreement over what non-normal distributions are plausible, is rare. The paper proposes a linear model that allows for trend versus difference stationarity and asymmetric behavior over the business cycle along with several distributional alternatives for the disturbance terms. It proposes computationally feasible Markov Chain Monte Carlo methods to perform Bayesian computations, applies the model to industrial production data of seven industrialized countries, and relies on prior predictive densities to compare models with Student- t , symmetric stable, EGARCH, exponential power family and finite-mixture-of-normals errors. The relationship between unit root inference, asymmetry and leptokurtosis is examined in detail using the exact, finite-sample posteriors corresponding to the different models.     

Statistical aspects of simulation: an updated survey*

Abstract Practical statistical techniques for the design and analysis of simulation experiments are presented. These techniques are relevant in both discrete and continuous, deterministic and stochastic simulation. To generalize and interpret the simulation output the analyst can use regression analysis. This analysis allows for interactions among factors. Actually the regression model provides either a first-order or a second-order approximation to the complicated simulation model. To decide which system variants (parameter combinations) should be simulated, the analyst may apply experimental design theory. This theory makes the exploration of the simulated system much more efficient and more thorough. In the preliminary phase of the simulation experimentation special screening designs can be used to investigate hundreds of factors in relatively few runs. In stochastic simulation additional problems arise. There are several approaches for determining how to initialize a simulation run and how long to continue that run. These approaches result in a confidence interval for the estimated response. Both steady-state and transient behavior are examined. Special variance reduction techniques are briefly discussed; the use of common random numbers (identical seeds) is discussed in more detail.