Highs and lows: Some properties of the extremes of a diffusion and applications in finance

Observations on security prices, currency exchange rates, interest rates, and other financial time series usually include not only an open and close, but also a high and low price for the period. For Brown‐ian motion and certain diffusion processes, the information on high and low prices is of considerable value, particularly for estimating volatility, correlations between processes, and in the pricing of look‐back and barrier options. For pricing more general derivatives, this information is useful to the extent that change in volatility is an important ingredient in the price. The author gives a simple geometric device for generating the extremes of Brownian motion, and geometric Brownian motion; he then uses these extremes in the estimation of the volatility of the processes and to study survivorship bias.     

A quadratically convergent algorithm for first passage time distributions in the Markov-modulated Brownian motion

A Markov-modulated Brownian motion (MMBM) is a substantial generalization of the classical Brownian Motion and is obtained by allowing the Brownian parameters to be modulated by an underlying Markov chain of environments. As with Brownian Motion, the time-dependent analysis of the MMBM becomes easy once the first passage times between levels are determined. However, in the MMBM those distributions cannot be obtained explicitly, and we need efficient algorithms to compute them. In this article, we provide a powerful approach based on approximating the MMBM with a sequence of scaled Markov-modulated fluid flows without Brownian components that weakly converge to the MMBM. Our main result is a Riccati equation for an associated matrix of transforms that satisfies conditions for the Newton scheme to have quadratic convergence and thus yields a very practical tool. The solution of that Riccati equation determines needed first passage times in the MMBM without much additional work. The success of our approach, which is based essentially on first-order fluid flows and a stochastic limit process, is argued to be due to the way we have isolated certain terms involving the quadratic variation effects of the Brownian. As an illustration of our algorithm, we present a numerical example of time-dependent results for a MMBM considered by Asmussen for which he determined (only) the eventual first return probabilities which we use here as an accuracy check.     

Adaptive trait evolution in random environment

Current phylogenetic comparative methods generally employ the Ornstein–Uhlenbeck(OU) process for modeling trait evolution. Being able of tracking the optimum of a trait within a group of related species, the OU process provides information about the stabilizing selection where the population mean adopts a particular trait value. The optima of a trait may follow certain stochastic dynamics along the evolutionary history. In this paper, we extend the current framework by adopting a rate of evolution which behave according to pertinent stochastic dynamics. The novel model is applied to analyze about 225 datasets collected from the existing literature. Results validate that the new framework provides a better fit for the majority of these datasets.     

Brownian Bridge and Other Path-dependent Gaussian Processes Vectorial Simulation

The iterative simulation of the Brownian bridge is well known. In this article, we present a vectorial simulation alternative based on Gaussian processes for machine learning regression that is suitable for interpreted programming languages implementations. We extend the vectorial simulation of path-dependent trajectories to other Gaussian processes, namely, sequences of Brownian bridges, geometric Brownian motion, fractional Brownian motion, and Ornstein–Ulenbeck mean reversion process.     

情绪表达性量表的质量分析

主要对由Krings,mith和Neale(1994)编制,陈会昌等译定的情绪表达性量表的信度和效度进行分析,结果显示,该量表的信度较高,共分离出三个因子:抑制情绪;乐于表达情绪;情绪表达不适。     

英汉虚构位移结构分析

虚构位移表达是对静态场景的一种动态表征形式。在虚构位移结构中,位移词用来描述并不发生实际运动的静态实体,在语言表层凸显静态实体的某种物理运动。利用Langacker认知语法中的射体(trajector)、路标(landm ark)来分析虚构位移的语言结构特点,可以发现隐现在语言结构中的观察者或其视线发生了位移,其中观察者采用顺序扫描来建构语义内容。     

情感符号中的审美人格——《文心雕龙》与《诗品》比较

《文心雕龙》和《诗品》有相近的情感符号：声律、夸饰、事类；又有相异的运动结构：刘勰以总论一枢纽一割情析采构建著作理论体系，钟嵘以三篇序文和60篇评品文章构筑著作结构。同时，情感符号扣理论结构蕴含文艺家的审美人格：刘勰追求“重旨复意”之无我，钟嵘崇尚“无极动心”之无味。     

近断层地震脉冲效应对大跨度桥梁地震响应的影响

历次震害表明，近断层地震的脉冲效应（滑冲 fling step和前导方向性 forward rupture directivity）使得大量土木工程结构产生灾难性的破坏。大跨度桥梁的动力特性决定了这两种不同的脉冲效应都将对其地震响应产生影响。通过选取具有典型脉冲效应的近断层地震记录，检查了三座不同类型的大跨度桥梁的地震响应,并探讨了脉冲效应的影响。结果表明：滑冲效应在长周期的大跨度桥梁关键部位产生数倍于一般地震的位移和内力响应，而加速度脉冲效应可能对位移响应并无太大影响，却对其内力响应具有与滑冲效应同等程度的影响；对于周期较短的拱桥结构，虽然滑冲效应对其部分长振动周期结构的位移响应具有较大的影响，但加速度脉冲对结构内力的影响更为显著。     

A new futility test approach in clinical interim data monitoring

Sequential monitoring of efficacy and safety data has become a vital component of modern clinical trials. It affords companies the opportunity to stop studies early in cases when it appears as if the primary objective will not be achieved or when there is clear evidence that the primary objective has already been met. This paper introduces a new concept of the backward conditional hypothesis test (BCHT) to evaluate clinical trial success. Unlike the regular conditional power approach that relies on the probability that the final study result will be statistically significant based on the current interim look, the BCHT was constructed based on the hypothesis test framework. The framework comprises a significant test level as opposed to the arbitrary fixed futility index utilized in the conditional power method. Additionally, the BCHT has proven to be a uniformly most powerful test. Noteworthy features of the BCHT method compared with the conditional power method will be presented. Copyright © 2012 John Wiley & Sons, Ltd.     

TESTING FOR CONTINUOUS LOCAL MARTINGALES USING THE CROSSING TREE

We present statistical tests for the continuous martingale hypothesis; that is, for whether an observed process is a continuous local martingale, or equivalently a continuous time‐changed Brownian motion. Our technique is based on the concept of the crossing tree. Simulation experiments are used to assess the power of the tests, which is generally higher than that of recently proposed tests using the estimated quadratic variation (i.e. realized volatility). In particular, the crossing tree shows significantly higher power with shorter data sets. We then show results from applying the methodology to five high‐frequency currency exchange rate data sets from 2003. For four of them we show that at small time‐scales (less than 15 minutes or so) the continuous martingale hypothesis is rejected, but not so at larger time‐scales. For the fifth, the hypothesis is rejected at small time‐scales and at some moderate time‐scales, but not all.