基于Mike Farmer委托驱动模型的研究

Mike-Farmer微观模型是功能强大的委托驱动模型,能再现很多经典的统计规律.本文介绍了Mike-Farmer委托驱动模型的构建过程,Mike-Farmer委托驱动模型生成的收益率,发现收益率在不同时间尺度下遵循幂律分布,服从负三次方定律.以Mike-Farmer委托驱动模型为平台,进行收益率幂律分布和波动率聚簇效应的成因研究,发现收益率的幂律分布和市价订单委托价格的概率分布相关,而波动率的聚簇效应与订单委托价格时间序列的时间记忆性保持一致性.最后简要介绍了模型的应用前景.     

相互作用herding模型的非线性行为和动力学特性

相互作用herding模型定性上能很好地呈现一些真实的经济规律,但定量上与真实的市场还有一定的距离,特别是收益绝对值的自关联衰退得太快．通过数值模拟研究发现该模型在它的参数取某些特定值时具有特有的非线性行为和动力学特性．此时,它不仅重现该模型原有的动力学特性,并能展现出更接近真实的市场规律,其中收益绝对值表现出长程关联,呈现出幂指数分布,它的幂明显变小,落在真实的市场规律范围内．     

基于q指数贴现函数的反按揭支付偏好研究

为研究人们对反按揭支付方式的偏好特征，分别建立基于指数函数和q指数函数的反按揭模型并求解.根据模型按照本金递减、本金不变和本金递增的还款方式设计三种反按揭合同并进行满意度调查，三种还款方式按指数函数估值相同，按q指数函数估值不同.对调查结果进行Kruskal-Wallis非参数检验发现:三种方式中，人们最偏好本金递增的还款方式，其次是本金不变，最次是本金递减的还款方式.结论显示金融企业可在不提高利率的情况下通过改变支付方式提高客户对反按揭的满意度.     

Universal laws and economic phenomena

Despite the idiosyncratic behavior of individuals, empirical regularities exist in social and economic systems. These regularities often arise from simple underlying mechanisms which, analogous to the natural sciences, can be expressed as universal principles or laws. In this essay, I discuss the similarities between economic and natural phenomena and argue that it is advantageous for economists to adopt methods from the natural sciences to discover “universal laws” in economic systems. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

金融市场的宏观建模和微观建模——从金融海啸与市场风险谈起

金融市场是一个复杂系统,高风险大波动危象频仍,而传统经济金融理论对此无能为力.文章从复杂性科学视角出发,通过市场宏观建模,描绘出当前金融海啸一幅泡沫演化和湮灭的图像.文章进一步论述了一个基于市场微观模型的计算实验金融学框架,认为金融学应当重建唯象学框架,并指出金融物理学在经济学科学革命中的重要性.     

Role of noise in a market model with stochastic volatility

We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.     

Leptokurtic portfolio theory

The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurtic, because it minimises the effects from “fat tails” of returns. The leptokurtic portfolio theory provides an optimal portfolio for investors, who define their risk-aversion as unwillingness to experience sharp drawdowns in asset prices. Two types of risks in asset returns are defined: a fluctuation risk, that has Gaussian distribution, and a drawdown risk, that deals with distribution tails. These risks are quantitatively measured by defining the “noise kernel” — an ellipsoidal cloud of points in the space of asset returns. The size of the ellipse is controlled with the threshold parameter: the larger the threshold parameter, the larger return are accepted for investors as normal fluctuations. The return vectors falling into the kernel are used for calculation of fluctuation risk. Analogously, the data points falling outside the kernel are used for the calculation of drawdown risks. As a result the portfolio optimisation problem becomes three-dimensional: in addition to the return, there are two types of risks involved. Optimal portfolio for drawdown-averse investors is the portfolio minimising variance outside the noise kernel. The theory has been tested with MSCI North America, Europe and Pacific total return stock indices.     

An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market

In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher order moments of a probability distribution function. An empirical application was made using data collected from the Portuguese Stock Market.     

Relaxation in statistical many-agent economy models

We review some statistical many-agent models of economic and social systems inspired by microscopic molecular models and discuss their stochastic interpretation. We apply these models to wealth exchange in economics and study how the relaxation process depends on the parameters of the system, in particular on the saving propensities that define and diversify the agent profiles.     

Convergence to an exponential wealth distribution in a random market model

We study the discrete-time model of López-Ruiz, López and Calbet, describing the evolution of a wealth distribution under random pairwise exchanges of wealth among agents. This requires the analysis of the behaviour of iterations of a non-linear operator defined on a space of probability distributions. We prove that, as conjectured by López-Ruiz, López and Calbet, starting from a general wealth distribution, the wealth distribution converges to the exponential equilibrium distribution. The proof employs a special metric defined on spaces of probability distributions through their Laplace transforms.