The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study

The effect on the estimation of the Value at Risk when dealing with multivariate portfolios when there is a misspecification both in the marginals and in the copulas is investigated. It is first shown that, when there is skewness in the data and symmetric marginals are used, the estimated elliptical (normal or t) copula correlations are negatively biased, reaching values as high as 70% of the true values. Besides, the bias almost doubles if negative correlations are considered, compared to positive correlations. As for the t copula degrees of freedom parameter, the use of wrong marginals delivers large positive biases, instead. If the dependence structure is represented by a copula which is not elliptical, e.g. the Clayton copula, the effects of marginal misspecifications on the copula parameter estimation can be rather different, depending on the sign of marginal skewness. Extensive Monte Carlo studies then show that the misspecifications in the marginal volatility equation more than offset the biases in copula parameters when VaR forecasting is of concern, small samples are considered and the data are leptokurtic. The biases in the volatility parameters are much smaller, whereas those ones in the copula parameters remain almost unchanged or even increase when the sample dimension increases. In this case, copula misspecifications do play a role for VaR estimation. However, these effects depend heavily on the sign of the dependence.     

Modeling and simulation of the market fluctuations by the finite range contact systems

In this paper, we model a new random stock price model for the stock markets based on the finite range contact process, which is a model for epidemic spreading that mimics the interplay of local infections and recovery of individuals, it is a member of a class of stochastic processes known as interacting particle systems. Then, we analyze the statistical behaviors of Shanghai Stock Exchange (SSE) Composite Index, Shenzhen Stock Exchange (SZSE) Composite Index, Dow Jones Industrial Average Index (DJIA), Nasdaq Composite Index (IXIC), the standard and Poor’s 500 Index (S&P500) and the simulative data derived from the finite range contact model by comparison. And six individual Chinese stocks from large-cap, mid-cap and small-cap categories are discussed. Furthermore, we investigate the long range correlations of the returns for these indices and the corresponding simulative data by applying the detrended fluctuation analysis. At last, the positive part of the probability distributions of the logarithmic returns for the actual data and the simulative data are studied by the q-Gaussian dynamic systems. The main objective of this work is to discuss the impact on the returns with the different range financial models.     

基于Intranet的高性能金融仿真平台建立和使用

Monte Carlo仿真是实现金融证券定价及风险评估的主要方法．本文提出在Intranet上利用JAVA简单、快速建立并行Monte Carlo仿真平台的方法．SPMD编程模型用于程序设计，利用eager算法实现负载均衡、容错及适度并行．独立序列作为并行伪随机数生成技术从而保证并行仿真的可用性．股票期权定价及银行信用风险VaR实时计算作为应用，完成实际仿真系统设计及实验．获得理想运行结果．目前，该平台及应用系统可用于金融机构创新服务和风险管理中．     

A detailed comparison of value at risk estimates

This work investigates the performance of different models of value at risk. We include several methods (parametric, historical simulation, Monte Carlo, and extreme value theory) and some models to compute the conditional variance. We analyze several international stock indexes and examine two types of periods: stable and volatile periods. To choose the best model, we employ a two-stage selection approach. The result indicates that the best model is a parametric model with conditional variance estimated by an asymmetric GARCH model under Student's t-distribution of returns. This paper shows that parametric models can obtain successful VaR measures if conditional variance is estimated properly.     

Likelihood-free Bayesian estimation of multivariate quantile distributions

In this paper, we present new multivariate quantile distributions and utilise likelihood-free Bayesian algorithms for inferring the parameters. In particular, we apply a sequential Monte Carlo (SMC) algorithm that is adaptive in nature and requires very little tuning compared with other approximate Bayesian computation algorithms. Furthermore, we present a framework for the development of multivariate quantile distributions based on a copula. We consider bivariate and time series extensions of the g-and-k distribution under this framework, and develop an efficient component-wise updating scheme free of likelihood functions to be used within the SMC algorithm. In addition, we trial the set of octiles as summary statistics as well as functions of these that form robust measures of location, scale, skewness and kurtosis. We show that these modifications lead to reasonably precise inferences that are more closely comparable to computationally intensive likelihood-based inference. We apply the quantile distributions and algorithms to simulated data and an example involving daily exchange rate returns.     

Quantile autoregression neural network model with applications to evaluating value at risk

We develop a new quantile autoregression neural network (QARNN) model based on an artificial neural network architecture. The proposed QARNN model is flexible and can be used to explore potential nonlinear relationships among quantiles in time series data. By optimizing an approximate error function and standard gradient based optimization algorithms, QARNN outputs conditional quantile functions recursively. The utility of our new model is illustrated by Monte Carlo simulation studies and empirical analyses of three real stock indices from the Hong Kong Hang Seng Index (HSI), the US S&P500 Index (S&P500) and the Financial Times Stock Exchange 100 Index (FTSE100).     

The impact of the dependence structure in risk management: a focus on credit-risk

The aim of the paper is to discuss the important role of the dependence structure in risk management. Therefore, we focus on credit-risk and propose an innovative model to value the credit risk of a portfolio. This new approach (HYC for short) is based on a hierarchical hybrid copula and involves a clusterization of the portfolio in several risk's classes. The HYC model is classified as hybrid because the computation of the loss cdf depends on the class's cardinality: for large groups one is justified to apply a limiting approach, while for small ones one applies a procedure preserving the granularity of the group itself. In order to appreciate the impact of the dependence structure in credit-risk evaluation, a VaR analysis based on the HYC loss function is here compared to the CreditMetrics approach in an in-sample exercise and to the empirical VaR in an out-of sample exercise aimed to test the forecasting effectiveness of the model. This comparison allows us to appreciate over/under-valuation of the capital detained from the financial institution. Moreover, the impact of an enlargement of the dependence structure is discussed with respect to the systemic/contagious effects in the context of a portfolio optimisation with constraint on a sub-portfolio's risk.     

Multistage portfolio optimization with stocks and options

We develop a multistage portfolio optimization model that utilizes options for mitigating market risk in a dynamic setting. Due to the key role of scenarios in the quality of investment decisions, a new scenario generation method is proposed that characterizes the dynamic behavior of asset returns. This methodology takes the dependence structure of different asset returns into account, and also considers serial correlations of each of the asset returns. Moreover, it preserves marginal distributions of asset returns. Also, it precludes arbitrage opportunities. To investigate the role of options, we implement the scenario generation method on a set of stocks selected from the New York Stock Exchange. Results show the high performance of the proposed scenario generation method. Afterwards, the generated set of scenarios is used as the uncertainty set for the multistage portfolio optimization model. Static and dynamic assessments are used for measuring the performance of options in mitigating market risks and generating additional returns. Finally, backtesting simulations are used for assessing different trading strategies of options.     

Estimating stochastic volatility models of stock returns in Chinese markets

Volatility plays a key role in microstructure issues in the study of financial markets. Stochastic volatility (SV) models have been applied to the study of the behavior of financial variables. Two stock markets exist in China: Shanghai Stock Exchange and Shenzhen Stock Exchange. As emerging stock markets, investors are increasingly concerned about the volatilities of these two stock markets. We briefly introduce how to estimate SV models using the Markov chain Monte Carlo (MCMC) method. In order to do full and comprehensive analyses of the volatilities of stock returns, we estimated SV models using most of the historical data and the different data frequencies of the two Chinese markets. We found that estimated values of volatility parameters are very high for all data frequencies. This suggests that stock returns are extremely volatile even at long-term intervals in Chinese markets.     

基于CVaR和Monte Carlo仿真的贷款组合决策模型

提供了一种新的贷款组合决策优化方法,该模型用更能反映贷款组合信用风险特征的CVaR作为风险度量。由于在实际中很难获取各笔贷款的历史数据,为此给出了一种基于Matlab语言的Monte Carlo仿真方法。从而使谊模型可以通过线性规划技术有效的进行求解。最后给出了一个例子。     

Multivariate reduced rank regression in non-Gaussian contexts, using copulas

A new procedure is proposed that performs reduced rank regression (RRR) in non-Gaussian contexts based on multivariate dispersion models. Reduced-rank multivariate dispersion models (RR-MDM) generalize RRR to a very large class of distributions, which include continuous distributions like the normal, Gamma, inverse Gaussian, and discrete distributions like the Poisson, the binomial and the negative binomial. A multivariate distribution is created with the help of the Gaussian copula and estimation is performed using maximum likelihood. It is shown how this method can be amended to deal with the case of discrete data. A Monte Carlo simulation shows that the new estimator is more efficient than the traditional Gaussian RRR. In the framework of MDM's a procedure analogous to canonical correlations is introduced, which takes into account the distribution of the data. Finally, the method is applied to the number of trades of five US department stores on the New York Stock Exchange during the year 1999 and determine the existence of a common factor which represents sector specific news. This analysis is helpful in microstructure analysis to identify leaders from the point of view of dissemination of sectorial information.     

Bayesian changepoint and time-varying parameter learning in regime switching volatility models

This paper proposes a combined state and piecewise time-varying parameter learning technique in regime switching volatility models using multiple changepoint detection. This approach is a Sequential Monte Carlo method for estimating GARCH & EGARCH based volatility models with an unknown number of changepoints. Modern auxiliary particle filtering techniques are used to calculate the posterior densities and online forecasts. This approach also automatically deals with the common ancestral path dependence problem faced in these type volatility models. The model is tested on Borsa Istanbul (BIST) formerly known as Istanbul Stock Exchange (ISE) market data using daily log returns. A full structural changepoint specification is defined in which all parameters of the conditional variance of the volatility models are dynamic. Finally, it is shown with simulation experiments that the proposed approach partitions the series into several regimes and learns the parameters of each regime's volatility model in parallel with the multiple changepoint detection process.     

基于神经网络集成学习股票预测模型的研究

基于深度学习的原理构建出六层长短记忆神经网络，通过集成学习中Bagging方法组合8个长短记忆神经网络。使用基于神经网络集成学习模型预测中国人民币普通股市场。实验测试了从2012年1月4日到2017年12月29日这期间的上海证券综合指数、深圳证券综合指数、上证50指数、沪深300指数、中小企业板指数和创业企业板指数。实验结果为模型的准确率达到58.5%，精确率为58.33%，召回率为73.5%，[F1]值为64.5%，AUC值为57.67%，取得了较好的预测效果。     

贷款组合信用风险模拟的简化方法

金融机构对贷款组合风险管理的通常方法是在VaR框架下,用蒙特卡罗模拟模拟技术估计期末贷款组合价值分布来计算最大损失.但模拟技术会产生极大的计算工作量.提出了运用计算机模拟技术对贷款组合信用风险(Value at Risk,VaR)的蒙特卡罗模拟进行简化的方法,把一个贷款组合在每个信用评级级别划分为子贷款组合,用同类子贷款组合的非预期损失来获得不同类子贷款组合的最大损失.以期节省运行时间,提高计算效率.模拟结果表明利用该方法计算贷款组合信用风险VaR效率高,能够较准确地获得信用风险值.     

Performance of a Hedged Stochastic Portfolio Model in the Presence of Extreme Events

Classical methods for computing the value-at-risk(VaR) do not account for the large price variationsobserved in financial markets. The historical methodis subject to event risk and may miss some fundamentalmarket evolution relevant to VaR; thevariance/covariance method tends to underestimate thedistribution tails and Monte Carlo simulation issubject to model risk. These methods are therebyusually completed with analyses derived fromcatastrophe scenarios.We propose a special case of the extreme-valueapproach for computing the value-at-risk of a stochasticmulticurrency portfolio when alternative hedgingstrategies are considered. This approach is able tocover market conditions ranging from the usual VaRenvironment to financial crises.We implement a multistage portfolio model with anexchange rate dynamic with stochastic volatility. Theparameters are estimated by GARCH-t models. Thesimulations are used to select multicurrencyportfolios whose exchange rate risk is hedged andrebalanced each ten days, accounting for VaR. Wecompare the performances of the two most classicalinstitutional options strategies – protective puts andcovered calls – to that of holding an unhedgedportfolio in presence of extreme events.     

C-Vine Pair Copula Based Wind Power Correlation Modelling in Probabilistic Small Signal Stability Analysis

The increasing integration of wind power generation brings more uncertainty into the power system. Since the correlation may have a notable influence on the power system, the output powers of wind farms are generally considered as correlated random variables in uncertainty analysis. In this paper, the C-vine pair copula theory is introduced to describe the complicated dependence of multidimensional wind power injection, and samples obeying this dependence structure are generated. Monte Carlo simulation is performed to analyze the small signal stability of a test system. The probabilistic stability under different correlation models and different operating conditions scenarios is investigated. The results indicate that the probabilistic small signal stability analysis adopting pair copula model is more accurate and stable than other dependence models under different conditions.      

Conditional copulas, association measures and their applications

One way to model a dependence structure is through the copula function which is a mean to capture the dependence structure in the joint distribution of variables. Association measures such as Kendall’s tau or Spearman’s rho can be expressed as functionals of the copula. The dependence structure between two variables can be highly influenced by a covariate, and it is of real interest to know how this dependence structure changes with the value taken by the covariate. This motivates the need for introducing conditional copulas, and the associated conditional Kendall’s tau and Spearman’s rho association measures. After the introduction and motivation of these concepts, two nonparametric estimators for a conditional copula are proposed and discussed. Then nonparametric estimates for the conditional association measures are derived. A key issue is that these measures are now looked at as functions in the covariate. The performances of all estimators are investigated via a simulation study which also includes a data-driven algorithm for choosing the smoothing parameters. The usefulness of the methods is illustrated on two real data examples.     

A feature weighted support vector machine and K-nearest neighbor algorithm for stock market indices prediction

This study investigates stock market indices prediction that is an interesting and important research in the areas of investment and applications, as it can get more profits and returns at lower risk rate with effective exchange strategies. To realize accurate prediction, various methods have been tried, among which the machine learning methods have drawn attention and been developed. In this paper, we propose a basic hybridized framework of the feature weighted support vector machine as well as feature weighted K-nearest neighbor to effectively predict stock market indices. We first establish a detailed theory of feature weighted SVM for the data classification assigning different weights for different features with respect to the classification importance. Then, to get the weights, we estimate the importance of each feature by computing the information gain. Lastly, we use feature weighted K-nearest neighbor to predict future stock market indices by computing k weighted nearest neighbors from the historical dataset. Experiment results on two well known Chinese stock market indices like Shanghai and Shenzhen stock exchange indices are finally presented to test the performance of our established model. With our proposed model, it can achieve a better prediction capability to Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index in the short, medium and long term respectively. The proposed algorithm can also be adapted to other stock market indices prediction.     

加权分布模型测算个股VaR

本文在同时考虑企业的个性风险和企业将受到整个国家宏观经济形势影响的共性风险的基础上．用一种新的思路定权数．提出了用加权分布测算个股VaR的模型。并以在深圳股市上市的四家企业的股票收益率做实证分析和模型检验。结果表明：加权分布提高了原来的假设收益率分布服从单一分布下测算VaR的准确度。尤其对于个性风险较强的企业而言。加权分布模型是一种形式简单。而又较为精确的模型.