A Stochastic Correlation Model with Mean Reversion for Pricing Multi-Asset Options

We set up a new kind of model to price the multi-asset options. A square root process fluctuating around its mean value is introduced to describe the random evolution of correlation between two assets. In this stochastic correlation model with mean reversion term, the correlation is a random walk within the region from −1 to 1, and it is centered around its equilibrium value. The trading strategy to hedge the correlation risk is discussed. Since a solution of high-dimensional partial differential equation may be impossible, the Quasi-Monte Carlo and Monte Carlo methods are introduced to compute the multi-asset option price as well. Taking a better-of two asset rainbow as an example, we compare our results with the price obtained by the Black–Scholes model with constant correlation.     

The augmented Black–Litterman model: a ranking-free approach to factor-based portfolio construction and beyond

The Fama and French factor-ranking approach (1992, 1993, etc.) has been extensively applied in quantitative fund management. However, this approach suffers from hidden factor view, information inefficiency, etc. issues. Based on the Black–Litterman model (1992; as explained in Cheung 2010b Cheung, W. 2010b. The Black–Litterman model explained. J. Asset Mgmt., 11: 229–243. [Crossref] , [Google Scholar]), we develop a technique that endogenizes the ranking process and elegantly resolves these issues. This model explicitly seeks forward-looking factor views and smoothly blends them to deliver robust allocation to securities. Our numerical experiments show this is an intuitive and practical framework for factor-based portfolio construction, and beyond. This article features: (1) a new and unified framework for strategy combination, factor mimicking and security-specific bets; (2) an elegant and ranking-free approach to factor style construction; (3) worked examples based on the FTSE EUROTOP 100 universe; (4) insight into the classic issue of confidence parameter setting; and (5) implementation guidance in an appendix.     

On Estimators of the Nearest Neighbour Distance Distribution Function for Stationary Point Processes

There are three approaches for the estimation of the distribution function D(r) of distance to the nearest neighbour of a stationary point process: the border method, the Hanisch method and the Kaplan-Meier approach. The corresponding estimators and some modifications are compared with respect to bias and mean squared error (mse). Simulations for Poisson, cluster and hard-core processes show that the classical border estimator has good properties; still better is the Hanisch estimator. Typically, mse depends on r, having small values for small and large r and a maximum in between. The mse is not reduced if the exact intensity λ (if known) or intensity estimators from larger windows are built in the estimators of D(r); in contrast, the intensity estimator should have the same precision as that of λ D(r). In the case of replicated estimation from more than one window the best way of pooling the subwindow estimates is averaging by weights which are proportional to squared point numbers.     

特质波动、风险溢价与学习效应

本文是一项实证研究,分析中国证券市场中股票特质波动性(Idiosyn-cratic Volatility)的风险溢价问题。我们发现较高波动性的投资组合在下一期收益率反而较低,为了解释这个看起来反常的现象,我们引入投资人逐步了解、发现上市公司盈利能力的学习过程。类似Lucas(1978)的一般均衡定价公式说明,不完全信息和学习过程会导致股票价格出现均值回归的现象(Mean Reversion),并且盈利能力不确定性越高的公司,股价向均值回归的趋势越明显,由此导致下一期收益率的反转。     

一种信号个数估计方法及其在测频中的应用

本文介绍一种高精度的数字测频算法———根MUSIC算法。通过分析发现,该算法在低信噪比(0 dB)的情况下,仍能得到高精度的频率估计值,其频率分辨率也比DFT高。然而,在电子侦察中要应用该方法进行测频,关键是首先要确定接收信号的个数。根据协方差矩阵特征值的大小分布特点,本文提出了差分中值法来确定信号个数,该方法的性能优于MDL准则。计算机仿真验证了该方法的可行性和稳健性。     

中国人力资本存量的估算：1952—2004年

由于统计资料的缺陷，中国至今没有完整的人力资本存量的数据。使用近似指标的替代只会造成经验研究结果的不可比性或结论的缺陷性。本文在现有统计资料的基础上，基于各阶段教育的毕业生数量，用永续盘存法估计了中国1952年到2004年的人力资本存量数据。最后，我们与相关研究做了对比分析。     

The norm game: punishing enemies and not friends

Three mean field models of the norm game are explored analytically. The strategies are: to obey the norm or not and to punish those who break it or not. The punishment, the temptation, the anger and the punishment cost are modeled by four parameters; for the fixed points, only two ratios of these parameters are relevant. For each model, we consider its variant with two mutually punishing groups. We show that all solutions are the same as for the case in one group. This means in particular, that in both groups the amount of defectors is the same.     

Best constants in Chebyshev inequalities with various applications

In this article we describe some ways to significantly improve the Markov-Gauss-Camp-Meidell inequalities and provide specific applications. We also describe how the improved bounds are extendable to the multivariate case. Applications include explicit finite sample construction of confidence intervals for a population mean, upper bounds on a tail probability P(X>k) by using the density at k, approximation of P-values, simple bounds on the Riemann Zeta function, on the series , improvement of Minkowski moment inequalities, and construction of simple bounds on the tail probabilities of asymptotically Poisson random variables. We also describe how a game theoretic argument shows that our improved bounds always approximate tail probabilities to any specified degree of accuracy. Received: April 1999     

An outer approximation algorithm for the robust shortest path problem

This paper describes a new algorithm for the stochastic shortest path problem where path costs are a weighted sum of expected cost and cost standard deviation. We allow correlation between link costs, subject to a regularity condition excluding unbounded solutions. The chief complication in this variant is that path costs are not an additive sum of link costs. In this paper, we reformulate this problem as a conic quadratic program, and develop an outer-approximation algorithm based on this formulation. Numerical experiments show that the outer-approximation algorithm significantly outperforms standard integer programming algorithms implemented in solvers.