Option pricing and perfect hedging on correlated stocks

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time τ0. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. With a modified portfolio consisting in calls, secondary calls and bonds we achieve a riskless strategy which results in a closed and exact expression for the European call price which is always lower than Black-Scholes price. We obtain the same price and a modified delta hedging if we start from an effective one-dimensional market model. We compare these strategies and study the sensitivity of the call price to several parameters where the correlation effects are also observed.     

Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.     

AR model whitening and signal detection based on GLD algorithm in the non-Gaussian reverberation

The paper analyzes the characteristics of shallow sea reverberation such as divergent variance and heavy tails in probability density distribution and matches it to symmetric alpha stable (SαS) distribution. After analyzing the AR model whitening method based on Gaussian distribution and Levinson–Durbin algorithm, the paper proposes and derives the generalized Levinson–Durbin (GLD) algorithm based on covariation theory of alpha stable distribution. The GLD algorithm can estimate the order and parameters of AR SαS model by iterations which are fast and effective in calculating, and then the performance tests by simulations are given. The AR model whitening method using GLD algorithm has a faster speed and a better detection performance than AR Gaussian whitening method in impulsive reverberation. At last the Monte Carlo simulating tests are used to validate the validity of the new method.     

High-order fuzzy time-series based on multi-period adaptation model for forecasting stock markets

Stock investors usually make their short-term investment decisions according to recent stock information such as the late market news, technical analysis reports, and price fluctuations. To reflect these short-term factors which impact stock price, this paper proposes a comprehensive fuzzy time-series, which factors linear relationships between recent periods of stock prices and fuzzy logical relationships (nonlinear relationships) mined from time-series into forecasting processes. In empirical analysis, the TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) and HSI (Heng Seng Index) are employed as experimental datasets, and four recent fuzzy time-series models, Chen’s (1996), Yu’s (2005), Cheng’s (2006) and Chen’s (2007), are used as comparison models. Besides, to compare with conventional statistic method, the method of least squares is utilized to estimate the auto-regressive models of the testing periods within the databases. From analysis results, the performance comparisons indicate that the multi-period adaptation model, proposed in this paper, can effectively improve the forecasting performance of conventional fuzzy time-series models which only factor fuzzy logical relationships in forecasting processes. From the empirical study, the traditional statistic method and the proposed model both reveal that stock price patterns in the Taiwan stock and Hong Kong stock markets are short-term.     

Anomalous scaling in a non-Gaussian random shell model for passive scalars

In this paper, we have introduced a shell-model of Kraichnan's passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and $\delta$ correlated in time, and its introduction is inspired by She and L\'{e}v\^{e}que (Phys. Rev. Lett. {\bf 72}, 336 (1994)). For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents $H(p)$ of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of $p$ up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the $H(p)$ advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.     

Impact of uncertainty in expected return estimation on stock price volatility

We investigate the origin of volatility in financial markets by defining an analytical model for time evolution of stock share prices. The defined model is similar to the GARCH class of models, but can additionally exhibit bimodal behaviour in the supply–demand structure of the market. Moreover, it differs from existing Ising-type models. It turns out that the constructed model is a solution of a thermodynamic limit of a Gibbs probability measure when the number of traders and the number of stock shares approaches infinity. The energy functional of the Gibbs probability measure is derived from the Nash equilibrium of the underlying game.     

Quantitative model of price diffusion and market friction based on trading as a mechanistic random process

We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.     

The roles of extrinsic periodic information on the stability of stock price

The perturbation expansion for the nonlinear Schrödinger equation with a random potential that was developed in earlier works by some of us is extended to higher orders. As the order is increased a solution that is valid for longer time can be found. In particular it is found that Anderson localization persists in the fifth and sixth orders for times when perturbation theory is valid. The perturbation expansion is asymptotic and for the value of the nonlinearity parameter used, the fifth order is the optimal order of the perturbation theory. There are indications that for the sixth order perturbation theory may not be valid.     

确定峰度非高斯海洋环境噪声模型研究

针对非高斯海洋环境噪声仿真问题,利用对衰减正弦信号均匀采样方法,产生了具有特定谱特性同时具有特定峰度值的非高斯海洋环境噪声序列。在理论仿真条件下,通过对低峰度值和高峰度值的分别讨论发现,当峰度值高于3.0时总可以仿真得到较好的结果,而当峰度值低于3.0时,需通过降采样或降阶的方法解决不能仿真的问题。4种海上试验条件下的仿真结果表明,在安静环境、单一航船干扰环境、气枪声源干扰环境以及冲击性干扰环境下,都可以产生与目标谱特性、统计特性几乎相同的非高斯海洋环境噪声序列。     

基于改进的对数周期幂律模型研究中国股市崩盘预警

基于金融物理学中著名的对数周期幂律模型(log-periodic power law model, LPPL)来预警2015年6月份中国上证综合指数、创业板指数的崩盘.鉴于已有采用LPPL模型预警市场崩盘的研究均只考虑市场历史交易数据.本文将投资者情绪因素纳入到LPPL模型建模过程,以改进LPPL模型的预警效果.采用文本挖掘技术结合语义分析方法对抓取的财经媒体的股评报道进行词频统计,以构建媒体情绪指数.进一步修改LPPL模型中的崩溃概率函数表达式,将其表示为关于历史交易数据及媒体情绪的函数,构建LPPL-MS组合模型预警股市崩盘.实证结果表明,本文所构建的LPPL-MS组合模型相比LPPL模型具有更高的预警精度,其预测的大盘见顶的临界时点与上证指数、创业板指数真实的见顶时点更为接近,并且其拟合结果通过了相关检验.     

一种简化非Gauss场模型在随机介质中光传播问题中的应用

为了研究大气湍流间歇性的光传播效应，构造出一种比较简单的非Gauss场模型(Poission场 )用于描述大气介电常数(或折射率)随机起伏.模型特征泛函含有四个待定函数，根据大气湍 流的统计均匀性，介电起伏的单点概率分布函数，以及介电起伏能谱可以选择或确定它们. 对在这种简化湍流中传播的光波平均场及二阶统计矩性质进行了理论分析，并给出数值模拟 的一个简单例子. 关键词： 光波传播 大气湍流 间歇性     

非高斯冲激干扰下基于Softplus函数的核自适应滤波算法

针对非高斯环境下一般自适应滤波算法性能严重下降问题,本文提出了一种基于Softplus函数的核分式低次幂自适应滤波算法(kernel fractional lower algorithm based on Softplus function,SP-KFLP),该算法将Softplus函数与核分式低次幂准则相结合,利用输...     

Effects of non-Gaussian noise on a calcium oscillation system

We investigate the effects of the non-Gaussian colored noise on a calcium oscillation system using stochastic simulation methods. It is found that the reciprocal coefficient of variance R has a maximum (R max ) with increasing noise intensity Q. The non-Gaussian noise parameter q has an important effect on the system. For some values of q (e.g., q = 0.9, q = 1.0), R has a maximum with increasing correlation time τ. Non-Gaussian noise induced spikes are more regular than Gaussian noise induced spikes when q is small and Q has large values. The R has a maximum with increasing q. Therefore, non-Gaussian noise could play more effective roles in the calcium oscillation system.     

Multiplicative non-Gaussian noise and additive Gaussian white noise induced transition in a piecewise nonlinear model

We study the transition problems in a piecewise nonlinear model induced by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Firstly, applying the path integral approach, the unified colored noise approximation, the analytical expression of the steady-state probability density function (SPD) is derived. Then the change regulation of the SPD is analyzed with the change of the strength and relevance of multiplicative noise and additive noise. From numerical computations we obtain some new nonlinear phenomena: the transition can be induced by the cross-correlation strength between noises, the non-Gaussian noise intensity and the Gaussian noise intensity as well as the non-Gaussian noise deviation parameter. This indicates that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. Moreover, we also find the correlation time of the non-Gaussian noise can not induce the transition.     

Recognition of gravitation impulses on a correlated non-Gaussian noise background

We consider the problem of gravitation-wave impulse recognition against the background of correlated noise produced by resonance gravitational antennas. A new algorithm for the joint processing of data recorded by spatially separated gravitational detectors is obtained. The algorithm is an alternative to the coincidence scheme, which is traditionally used in gravitation-wave experiments. It is based on the principles, well known in statistical radiophysics, of joint detection and parameter estimation in quasi-deterministic signals.     

Experimental implementation of non-Gaussian attacks on a continuous-variable quantum-key-distribution system

An intercept-resend attack on a continuous-variable quantum-key-distribution protocol is investigated experimentally. By varying the interception fraction, one can implement a family of attacks where the eavesdropper totally controls the channel parameters. In general, such attacks add excess noise in the channel, and may also result in non-Gaussian output distributions. We implement and characterize the measurements needed to detect these attacks, and evaluate experimentally the information rates available to the legitimate users and the eavesdropper. The results are consistent with the optimality of Gaussian attacks resulting from the security proofs.     

非高斯噪声激励下含周期信号FitzHugh-Nagumo系统的响应特征

研究了非高斯噪声激励下含周期信号的FHN模型的动力学行为. 通过计算神经元的平均响应时间、观察神经元的共振活化和噪声增强稳定现象,分析了非高斯噪声对神经元动力学行为的影响. 发现通过改变非高斯噪声的相关时间可以有效地改变共振活化和噪声增强稳定现象. 观察到在强相关噪声下不同强度的非高斯噪声抑制了神经元的噪声增强稳定现象而共振活化现象几乎不变,也就是非高斯噪声有效地增强了神经响应的效率. 观察了平均响应时间与非高斯噪声参数q之间的关系,当q为一个有限的小于1的值时,平均响应时间取得最小值. 最后表明在一定条件下,非高斯噪声出现重尺度现象,即非高斯噪声产生的效果可以由高斯白噪声来估计. 关键词： FHN神经系统 非高斯噪声 平均响应时间 共振活化现象     

Partial derivative approach for option pricing in a simple stochastic volatility model

We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model has already been introduced in the literature. We present a new approach to the problem, based on partial differential equations, which gives a different perspective to the issue. Within our framework we can easily consider several forms for the market price of volatility risk, and interpret their financial meaning. We thus recover solutions previously mentioned in the literature as well as obtaining new ones.Received: 13 May 2004, Published online: 26 November 2004PACS: 02.30.Jr Partial differential equations - 02.50.Ey Stochastic processes - 02.70.Uu Applications of Monte Carlo methods - 89.65.Gh Economics; econophysics, financial markets, business and management     

基于斑马鱼图像特征的鱼群检测算法北大核心CSCD

计算机视觉方法越来越多地应用于斑马鱼的群体行为研究;但是,由于斑马鱼游动过程形体变化大,遮挡多,准确与鲁棒地检测出斑马鱼仍然是一件非常具有挑战性的问题。为了解决该问题,提出一种基于斑马鱼图像特征的鱼群检测算法。首先通过分析目标特性,提出使用鱼头和鱼尾替代全鱼的检测方法,解决了传统整鱼检测在鱼群交叉遮挡时失效的难题;然后基于斑马鱼图像特征自动构建训练集,避免了深度学习手动标注的费时费力问题。通过对实际斑马鱼视频进行处理验证,与现有的算法相比,本文提出的方法在标注率、召回率(recall,R)与遮挡检测率(occlusion detection rate,ODR)等性能指标上有更好的实验效果。其中,在标注性能方面,本文提出的自动标注方法在总标注率上达到87.40%;在训练集效果方面,本文自动标注算法结合人工校正在标注时间上相比于人工标注方法减少93.11%,均值平均精度(mean average precision,mAP)达到79.80%;在目标检测方面,在目标遮挡率为42.72%的情况下,本文检测算法能够获得82.0%的召回率及58.02%的遮挡检测率。