Hedging of the European option in discrete time under proportional transaction costs

In the paper hedging of the European option in a discrete time financial market with proportional transaction costs is studied. It is shown that for a certain class of options the set of portfolios which allow to hedge an option in a discrete time model with a bounded set of possible changes in a stock price is the same as the set of such portfolios, under assumption that the stock price evolution is given by a suitable CRR model.     

Heterogeneous trading agents

In this article, we present a multiagent system (MAS) simulation of a financial market and investigate the requirements to obtain realistic data. The model consists of autonomous, interactive agents that buy stock on a financial market. Transaction decisions are based on a number of individual and collective elements, the former being risk aversion and a set of decision rules reflecting their anticipation of the future evolution of prices and dividends and the latter the information arriving on the market influencing the decision making process of each trader. We specifically look at this process and the following observations hold: The market behavior is determined by the information arriving at the market and agent heterogeneity is required in order to obtain the right statistical properties of the price and return time series. The observed results are not sensitive to changes in the parameter values. © 2003 Wiley Periodicals, Inc.     

Multi‐period mean variance portfolio selection under incomplete information

This paper solves an optimal portfolio selection problem in the discrete‐time setting where the states of the financial market cannot be completely observed, which breaks the common assumption that the states of the financial market are fully observable. The dynamics of the unobservable market state is formulated by a hidden Markov chain, and the return of the risky asset is modulated by the unobservable market state. Based on the observed information up to the decision moment, an investor wants to find the optimal multi‐period investment strategy to maximize the mean‐variance utility of the terminal wealth. By adopting a sufficient statistic, the portfolio optimization problem with incompletely observable information is converted into the one with completely observable information. The optimal investment strategy is derived by using the dynamic programming approach and the embedding technique, and the efficient frontier is also presented. Compared with the case when the market state can be completely observed, we find that the unobservable market state does decrease the investment value on the risky asset in average. Finally, numerical results illustrate the impact of the unobservable market state on the efficient frontier, the optimal investment strategy and the Sharpe ratio. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal portfolio strategies benchmarking the stock market

The paper investigates the impact of adding a shortfall risk constraint to the problem of a portfolio manager who wishes to maximize his utility from the portfolios terminal wealth. Since portfolio managers are often evaluated relative to benchmarks which depend on the stock market we capture risk management considerations by allowing a prespecified risk of falling short such a benchmark. This risk is measured by the expected loss in utility. Using the Black–Scholes model of a complete financial market and applying martingale methods, explicit analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.     

Option prices under stochastic volatility

The well known Heston model for stochastic volatility captures the reality of the motion of stock prices in our financial market. However, the solution of this model is expressed as integrals in the complex plane and has difficulties in numerical evaluation. Here, we present closed-form solutions for option prices and implied volatilities in terms of series expansions. We show that our theoretical predictions are in remarkably good agreement with numerical solutions of the Heston model of stochastic volatility.     

中国股市和债市波动溢出效应的MV-GARCH分析

股市和债市的波动溢出效应是研究金融市场信息流动、风险传递的重要内容。在估计了股市和债市候选MV-GARCH模型参数基础上,通过AIC准则等拟合优度方法选择了t分布型BEKK为最优模型,因为它更好的捕捉到了金融时序尖峰、厚尾的特征.结果显示,中国股市和债市波动溢出具有明显时变特征,波动影响不对称,股市对债市影响大于债市对股市影响。动态相关系数偏弱说明两个市场在资源配置能力、信息流动等方面存在显著的缺陷.     

基于混合跳扩散模型的最优投资消费和寿险购买策略研究

本文研究在混合跳扩散模型下投资者分别投资于寿险、零息债券和股票时,关于最优投资消费和寿险购买的随机策略问题。通过构造满足混合跳扩散模型的金融市场、保险市场和可容许策略,在CRRA(constant relative risk aversion)效用下,利用动态规划的方法求解了对应的HJB方程,获得了值函数和最优策略的显式表达式。为了探索模型的有效性,本文给出了相对风险厌恶系数的数值分析以及相关参数对最优策略的影响。     

Detection of multiple change-points in multivariate time series

We consider the multiple change-point problem for multivariate time series, including strongly dependent processes, with an unknown number of change-points. We assume that the covariance structure of the series changes abruptly at some unknown common change-point times. The proposed adaptive method is able to detect changes in multivariate i.i.d., weakly and strongly dependent series. This adaptive method outperforms the Schwarz criteria, mainly for the case of weakly dependent data. We consider applications to multivariate series of daily stock indices returns and series generated by an artificial financial market. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 351–376, July–September, 2006.     

我国汽车类样本上市公司股改事件窗中的风险与绩效评估

股权分置改革是中国股票市场的一场革命及重要的金融事件,它能够推动资本市场的改革,选取了两个具有代表性已实施股权分置改革的集团公司:上海汽车和宝利来.分别对两个集团公司在股改事件窗中的股票收益序列建立了合适的GARCH类模型.通过模型的实证结果得出股改后上海汽车和宝利来的收益水平均有很大的提高,而且股票价格波动对信息的反应更加灵敏,我国股票市场有效化程度显著提高.     

基于LMSV模型的半参数方法对股市波动长记忆特征的识别

在金融时间序列波动具有显著的长记忆性这一背景之下,研究了LMSV模型长记忆参数的估计问题。首先,分析了LMSV模型的相关性质;接着,根据LMSV模型和ARFIMA模型的良好对应关系,提出了估计LMSV模型长记忆参数的半参数方法;最后,基于股市数据,验证了波动半参数方法的有效性。     

逐段非趋势波动分析方法及我国证券市场的实证研究

为了研究金融时间序列在不同时段波动的持久性特征,本文提出了一种逐段非趋势波动分析方法。该方法首先建立多阶段分割动态规划模型对时间序列进行分割,随后对各子序列逐段进行非趋势波动分析。对我国证券市场的七个主要指数的实证研究结果表明,本文提出的逐段非趋势波动分析方法能够有效揭示股票指数持久性特征随时间变化的现象,也有助于更深入的比较不同指数间持久性特征的相似程度。     

广义双曲线分布模型在我国证券市场风险度量中的应用研究

经济的全球化、衍生产品的大量出现以及因此导致的金融市场的动荡使得金融机构越来越需要更有效的风险管理方法。而如何精确度量风险是风险管理的关键问题。本文试图从金融收益分布假设着手改善风险度量的精度。国外学者研究发现广义双曲线分布比其它分布形式可以更好地拟合实际收益分布特征。本文首次把广义双曲线分布应用到VaR的分析方法中计算我国股票指数的VaR。实证结果表明，基于广义双曲线分布的方法得到了较好的预测结果。     

金融风险在股票市场的传染效应及联动行为分析

近年来金融危机频发并表现出了易传染性,引起了众多学者的高度关注。以动态条件相关模型研究美欧股市与中、日、韩股市间的时变相关性,并结合内生多重结构突变模型划分危机传染阶段,选用溢出指数模型分析股市间的风险溢出特性;随后,定义股市间相互影响的联动模式并构建不同传染阶段的加权有向网络图分析股市间的联动行为。研究表明:美欧股市对中日韩股市有明显的传染效应,被传染的速度和持续时间均不相同;金融传染和风险溢出展现出一定的不一致性,危机期间日股的风险溢出效应强于美股;传染效应在联动网络中表现为联动模式的高聚类性和高联动性,相比欧债危机,次贷危机时期股市间展现出更强的联动行为;日股与美欧股市在两次危机中均表现出最强的联动性,其所受影响也最大。     

股票价格遵循几何分式Brown运动的期权定价

讨论了股票价格过程遵循几何分式B row n运动的欧式期权定价.由于该过程存在套利机会使得传统的期权定价方法(如资本资产定价模型(CAPM),套利定价模型(APT),动态均衡定价理论(DEPT))不可能对该期权定价.利用保险精算定价法,在对市场无其它任何假设条件下,获得了欧式期权的定价公式.并讨论了在有效期内股票支付已知红利和红利率的推广公式.     

Stock market forecasting by using a hybrid model of exponential fuzzy time series

The initial aim of this study is to propose a hybrid method based on exponential fuzzy time series and learning automata based optimization for stock market forecasting. For doing so, a two-phase approach is introduced. In the first phase, the optimal lengths of intervals are obtained by applying a conventional fuzzy time series together with learning automata swarm intelligence algorithm to tune the length of intervals properly. Subsequently, the obtained optimal lengths are applied to generate a new fuzzy time series, proposed in this study, named exponential fuzzy time series. In this final phase, due to the nature of exponential fuzzy time series, another round of optimization is required to estimate certain method parameters. Finally, this model is used for future forecasts. In order to validate the proposed hybrid method, forty-six case studies from five stock index databases are employed and the findings are compared with well-known fuzzy time series models and classic methods for time series. The proposed model has outperformed its counterparts in terms of accuracy.     

GARCH模型对上海股市的一个实证研究

GARCH模型是近20年发展起来的时间序列模型，它反映了经济变量之间特殊的不确定形式：方差随时间变化而变化，所以其在金融市场的预测与决策方面有着重要的作用。本文详细介绍了GARCH模型以及其主要变形，并建立了基于t分布和正态分布假设的GARCH（1，1）模型对股票市场进行了风险分析。结果表明，基于t分布的假设能更准确地拟和GARCH（1，1）模型。     

The geometry of relative arbitrage

Consider an equity market with n stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio representing the performance of the entire stock market. Consider a function that assigns a portfolio vector to each possible value of the market weight, and we perform self-financing trading using this portfolio function. We study the problem of characterizing functions such that the resulting portfolio will outperform the market portfolio in the long run under the conditions of diversity and sufficient volatility. No other assumption on the future behavior of stock prices is made. We prove that the only solutions are functionally generated portfolios in the sense of Fernholz. A second characterization is given as the optimal maps of a remarkable optimal transport problem. Both characterizations follow from a novel property of portfolios called multiplicative cyclical monotonicity.     

Fractal market hypothesis and two power-laws

A fractal approach is used to analyze financial time series by applying different degrees of time resolutions. This leads to the heterogenous market hypothesis (HMH), where different market participants analyze past events and news with different time horizons. A new general model for asset returns is studied in the framework of the fractal market hypothesis (FMH). It concerns capital market systems in which the conditionally exponential dependence (CED) property can be attached to each investor on the market.     

An extension of the Clark–Haussmann formula and applications

ABSTRACT

This work considers a financial market stochastic model where the uncertainty is driven by a multidimensional Brownian motion. The market price of the risk process makes the transition between real world probability measure and risk neutral probability measure. Traditionally, the martingale representation formulas under the risk neutral probability measure require the market price of risk process to be bounded. However, in several financial models the boundedness assumption of the market price of risk fails; for example a financial market model with the market price of risk following an Ornstein–Uhlenbeck process. This work extends the Clark–Haussmann representation formula to underlying stochastic processes which fail to satisfy the standard requirements. Our methodology is classical, and it uses a sequence of mollifiers. Our result can be applied to hedging and optimal investment in financial markets with unbounded market price of risk. In particular, the mean variance optimization problem can be addressed within our framework.     

基于GAS t-Copula模型的金融市场非对称风险溢出效应测度研究

准确测度金融风险溢出效应对于金融风险管理和构建投资组合具有重要意义,而金融市场之间的非线性及动态相关结构一直是风险溢出效应研究中的难点问题之一。本文通过引入GAS t-copula模型与CoVaR方法,结合能够刻画重要典型事实特征的边缘分布模型,构建了金融市场间的风险溢出效应测度模型,以中国内地等五个股市为研究对象,测度美国股市对中国内地等四个重要股市的风险溢出效应,以检验模型的可靠性与准确性。实证结果表明:中国内地等四个股市与美国股市之间呈现出显著为正且时变相关结构,随着金融危机的爆发,相关系数逐渐增加达到最大值;中国内地等四个股市受到美国股市的风险溢出效应呈现出非对称特征,即下跌风险溢出效应强度显著大于上涨风险溢出效应;中国内地股市受到的金融风险溢出效应显著小于香港、日本以及英国股市。