Energy portfolio risk management using time-varying extreme value copula methods

This work is concerned with the statistical modeling of the dependence structure between three energy commodity markets (WTI crude oil, natural gas and heating oil) using the concept of copulas and proposes a method for estimating the Value at risk (VaR) of energy portfolio based on the combination of time series models with models of the extreme value theory before fitting a copula. Each return series is modeled by AR-(FI) GARCH univariate model. Then, we fit the GPD distribution to the tails of the residuals to model marginal residuals distributions. The extreme value copula to the iid residuals is fitted and we simulate from it to construct N portfolios and estimate VaR. As a first step, the method is applied to a two-dimensional energy portfolio. In second step, we extend method in trivariate context to measure VaR of three-dimensional energy portfolio. Dependences between residuals are modeled using a trivariate nested Gumbel copulas. Methods proposed are compared with various univariate and multivariate conventional VaR methods. The reported results demonstrate that GARCH-t, conditional EVT and FIGARCH extreme value copula methods produce acceptable estimates of risk both for standard and more extreme VaR quantiles. Generally, copula methods are less accurate compared with their predictive performances in the case of portfolio composed of exchange market indices.     

VaR模型在套期保值比率计算中的实证分析

提出了考虑套期保值期内不同期限价格风险的最小平均VaR套期保值比率计算模型。基于我国外汇市场及股票市场数据,用最小平均VaR套期保值模型进行了实证分析,并同常用的最小方差及最小VaR套期保值模型进行了对比,得出了最小平均VaR模型在套期保值过程中的效果要优于其他两种模型,并能更有效地降低投资者提前终止套期保值可能面临额外风险的结论。     

A novel nonlinear value-at-risk method for modeling risk of option portfolio with multivariate mixture of normal distributions

This paper proposes a novel nonlinear model for calculating Value-at-Risk (VaR) when the market risk factors of an option portfolio are heavy-tailed. A multivariate mixture of normal distributions is used to depict the heavy-tailed market risk factors and accordingly a closed form expression for the moment generating function that can reflect the change in option portfolio value can be derived. Moreover, in order to make use of the correlation between the characteristic function and the moment generating function, Fourier-Inversion method and adaptive Simpson rule with iterative algorithm of numerical integration into the nonlinear VaR model for option portfolio are applied for calculation of VaR values of option portfolio. VaR values of option portfolio obtained from different methods are compared. Numerical results of Fourier-Inversion method and Monte Carlo simulation method show that high accuracy VaR values can be obtained when risk factors have multivariate mixture of normal distributions than when they have normal distributions. Moreover, VaR values obtained by using the Fourier-Inversion method are not obviously different from VaR values obtained by using Monte Carlo simulation when market risk factors have normal distributions or multivariate mixture of normal distributions. However, the speed of computation is obviously faster when using Fourier-Inversion method, than when using Monte Carlo simulation method. Besides, Cornish Fisher method is faster and simpler than Monte Carlo simulation method or Fourier-Inversion method. However, this method does not offer high accuracy and cannot be used to calculate VaR values of option portfolio when market risk factors have heavy-tailed distributions.     

An Economic Evaluation of Model Risk in Long‐term Asset Allocations

Following the recent crisis and the revealed weakness of risk management practices, regulators of developed markets have recommended that financial institutions assess model risk. Standard risk measures, such as the value‐at‐risk (VaR), emerged during the 1990s as the industry standard for risk management and become today a key tool for asset allocation. This paper illustrates and estimates model risk, and focuses on the evaluation of its impact on optimal portfolios at various time horizons. Based on a long sample of US data, the paper finds a non‐linear relation between VaR model errors and the horizon that impacts optimal asset allocations.     

我国主要证券市场VaR模型变动性研究

对证券市场风险度量模型的探索,一直是国内外金融风险管理者关注和研究的热点之一。VaR(Value-at-Risk)风险度量模型,目前已成为金融机构、非金融企业、金融监管部门测量和监控市场风险的主流工具。然而VaR模型能否有效正确地度量证券市场风险,不但取决于估计的精度,还取决于选用VaR模型本身的变动性。因此,探索我国主要证券市场VaR模型的变动性,有一定的现实意义。针对我国主要证券市场指数,本文首先通过图形展示了三类(参数、半参数和非参数)VaR估计方法在不同的窗口设定下控制风险的表现;其次在平均相对偏差(MRB)和平方根相对偏差(RMSRB)的双重标准下,对三类VaR估计模型的变动性进行了比较研究,结果表明:在我国主要证券市场上,参数类VaR估计模型本身的变动性和偏离程度较小,半参数类VaR估计模型次之,而非参数类VaR估计模型本身的变动性和偏离程度较大,这在一定程度上符合新兴国家证券市场存在较大投机收益的特点。     

Portfolio allocation and international risk sharing

Abstract We show that recent explanations of the consumption‐real exchange rate anomaly that rely on goods and financial market frictions are not robust to introducing just one additional international asset. When portfolios are selected optimally, international trade in two nominal bonds implies a consumption‐real exchange rate correlation that is too high compared with the data even when there are many shocks. Monetary policy specification plays a potentially important role for the degree of risk sharing provided by nominal bonds, both in the benchmark model with only tradable and non‐tradable sector supply shocks and also in the model that allows for news.     

Markets liquidity risk under extremal dependence: Analysis with VaRs methods

Value-at-Risk (VaR) is a widely used tool for assessing financial market risk. In practice, the estimation of liquidity extreme risk by VaR generally uses models assuming independence of bid–ask spreads. However, bid–ask spreads tend to occur in clusters with time dependency, particularly during crisis period. Our paper attempts to fill this gap by studying the impact of negligence of dependency in liquidity extreme risk assessment of Tunisian stock market. The main methods which take into account returns dependency to assess market risk is Time series–Extreme Value Theory combination. Therefore we compare VaRs estimated under independency (Variance–Covariance Approach, Historical Simulation and the VaR adjusted to extreme values) relatively to the VaR when dependence is considered. The efficiency of those methods was tested and compared using the backtesting tests. The results confirm the adequacy of the recent extensions of liquidity risk in the VaR estimation. Therefore, we prove a performance improvement of VaR estimates under the assumption of dependency across a significant reduction of the estimation error, particularly with AR (1)-GARCH (1,1)-GPD model.     

Intraday hedging with financial options: the case of electricity

As market intermediaries, electricity suppliers purchase electricity from the wholesale market or self-generate to deliver their customers. However, electricity suppliers are uncertain about how much electricity their residential customers will use at any hour of the day until they actually turn switches on. While demand uncertainty is a common feature of all commodity markets, suppliers generally rely on storage to manage it. Singularly, electricity suppliers are exposed to joint volumetric and price risk on an hourly basis given the physical attributes of electricity. In the literature on electricity markets, few articles compare the efficiency of forward contracts, options and physical assets (i.e. power plants) within intraday hourly hedging portfolios, whereas electricity markets are precisely hourly markets. We analyse portfolios made of forwards, options and/or power plants for specific hourly clusters (9 am, 12 pm, 18 pm, 9 pm) based on electricity market data from 2013 to 2015 from the integrated German–Austrian spot market. Through a VaR model, we prove that intraday hedging with forwards is structurally inefficient compared to financial options and physical assets, no matter the cluster hour. Moreover, our results demonstrate the contribution of ‘out of the money’ options for all hours within volatile spot markets.     

Overnight exchange rate risk based on multi-quantile and joint-shock CAViaR models

Overnight risk of exchange rate is more and more important because the exchange rate trading time of various countries is inconsistent. Drawing on the multi-quantile CAViaR model for two markets, this study proposes a multi-quantile CAViaR model for three markets and a multi-quantile CAViaR model for joint shock. The two new models are used to measure the impact of the U.S. Dollar index and the Euro on the overnight risk for the exchange rate of the Japanese Yen, Hong Kong Dollar, and Chinese Renminbi. The results show that, first, a lag risk affects the overnight risk of the three exchange rates, of which the Renminbi exchange rate is subject to the largest risk. Second, the U.S. Dollar index and Euro exchange rate risks impact the overnight risk of the three exchange rates and this effect is highest for the overnight risk of the Yen's exchange rate. In addition, the impact of the U.S.Dollar index risk is greater than that of the Euro. Third, the Euro and U.S.Dollar index produce a joint shock on the overnight risk of the three exchange rates, and here, the Yen's exchange rate suffers the biggest shock. Finally, the multi-quantile CAViaR model for joint shock is more accurate than that for three markets, particularly when the Hong Kong Dollar exchange rate has a 5% VaR. These empirical results have meaningful implications for regulatory authorities.     

Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns

This paper is concerned with linear portfolio value-at-risk (VaR) and expected shortfall (ES) computation when the portfolio risk factors are leptokurtic, imprecise and/or vague. Following Yoshida (2009), the risk factors are modeled as fuzzy random variables in order to handle both their random variability and their vagueness. We discuss and extend the Yoshida model to some non-Gaussian distributions and provide associated ES. Secondly, assuming that the risk factors' degree of imprecision changes over time, original fuzzy portfolio VaR and ES models are introduced. For a given subjectivity level fixed by the investor, these models allow the computation of a pessimistic and an optimistic estimation of the value-at-risk and of the expected shortfall. Finally, some empirical examples carried out on three portfolios constituted by some chosen French stocks, show the effectiveness of the proposed methods.     

我国银行间债券回购市场利率风险的实证研究

为提高我国银行间债券回购市场利率风险测定的准确性和实用性,本文针对我国银行间债券回购市场隔夜回购利率进行了基本特征分析,探讨了如何利用混合正态分布对利率数据进行拟合并据此计算VaR;作为对比组,本文同时采用GARCH模型族对利率数据进行处理。实证结果表明:与GARCH模型族相比,混合正态分布拟合方法计算VaR在准确性和实用性方面均有所提高。     

涉外企业的汇率风险度量

汇率风险日益成为影响涉外企业价值的重要因素,然而与对利率风险、信用风险的度量研究相比,汇率风险的度量研究相对滞后。本文通过尝试着把主要用来衡量利率风险的VaR方法运用于对涉外企业的汇率风险衡量,以期来推动理论界对汇率风险度量问题的关注。     

Backtesting VaR in consideration of the higher moments of the distribution for minimum-variance hedging portfolios

The higher moments of a distribution often lead to estimated value-at-risk (VaR) biases. This study's objective is to examine the backtesting of VaR models that consider the higher moments of the distribution for minimum-variance hedging portfolios (MVHPs) of the stock indices and futures in the Greater China Region for both short and long hedgers. The results reveal that the best backtesting VaR for the MVHP considered both the higher moments of the MVHP distribution and the asymmetry in volatility, cross-market asymmetry in volatility, and level effects in the covariance matrix of assets in the MVHP. These empirical results provide references for investors in risk management.     

最小平均VaR套期保值比率计算模型及实证研究

针对传统的套期保值模型只考虑最小化套期保值组合在到期日的价格风险,而且没有充分利用资产历史价格样本数据所提供的收益率信息的特点,本文提出了考虑套期保值期内不同期限价格风险的最小平均VaR套期保值比率计算模型。基于我国外汇市场及股票市场数据,本文对最小平均VaR套期保值模型进行了实证分析,并与常用的最小方差及最小VaR套期保值模型进行了对比,得出了最小平均VaR模型在套期保值过程中的效果要优于其他两种模型,能更有效地降低投资者提前终止套期保值可能面临额外风险的结论。     

基于VaR的沪深300股指期货风险管理实证研究

我国以沪深300为标的指数的股指期货即将推出。股指期货在具有控制风险功能的同时,也与其他金融衍生产品一样,具有风险性,且其风险远远大于股票现货市场。因此,必须采用积极的风险管理技术,加强对股指期货的风险防范。在GARCH模型的基础上,采用VaR方法对我国的沪深300股指期货仿真交易进行定量研究,计算出它们的VaR值,并将其与期望值进行比较。经过对比分析可以得出:基于GARCH模型的VaR方法适合我国的股指期货风险管理。     

标准仓单质押组合的价格风险——基于中国农产品期货规范市场的实证研究

利用基于Copula函数的AR(p)-GARCH(p,q)模型计算的VaR能够对农产品标准仓单的价格风险进行准确度量。对大连商品交易所的典型期货交易品种——黄大豆一号、豆油、豆粕的期货合约日结算价进行了实证研究。研究结果显示:从对价格风险预测的盯市频率来看,时变VaR优于静态VaR,因此重视农产品价格风险的频次预测应替代传统风险判断的单次监测;从对风险因子间相依性结构的刻画来看,基于t-Copula函数计算的VaR优于基于正态Copula函数计算的VaR,因此质押物价格波动间的相关系数是度量组合风险时必须考虑的重要变量。     

Exchange rate dynamics under gradual portfolio adjustment

This paper generalizes the asset market approach to exchange rate determination by introducing gradual adjustment of asset-holder portfolios. The influence of different speeds of portfolio adjustment on exchange rate dynamics is considered. Asset market models characterized by instantaneous portfolio equilibrium appear as a special case. The dynamics of exchange rate adjustment following an open-market operation are shown to be qualitatively similar to those of the orthodox instantaneous portfolio equilibrium models. Thus, gradual portfolio adjustment does not compromise the qualitative results derived with the help of those models. The speed of portfolio adjustment is however shown to influence the degree of exchange rate volatility. In particular, the phenomenon of exchange rate overshooting depends crucially on the speed of portfolio adjustment.     

Risk assessment of oil price from static and dynamic modelling approaches

The price gap between West Texas Intermediate (WTI) and Brent crude oil markets has been completely changed in the past several years. The price of WTI was always a little larger than that of Brent for a long time. However, the price of WTI has been surpassed by that of Brent since 2011. The new market circumstances and volatility of oil price require a comprehensive re-estimation of risk. Therefore, this study aims to explore an integrated approach to assess the price risk in the two crude oil markets through the value at risk (VaR) model. The VaR is estimated by the extreme value theory (EVT) and GARCH model on the basis of generalized error distribution (GED). The results show that EVT is a powerful approach to capture the risk in the oil markets. On the contrary, the traditional variance–covariance (VC) and Monte Carlo (MC) approaches tend to overestimate risk when the confidence level is 95%, but underestimate risk at the confidence level of 99%. The VaR of WTI returns is larger than that of Brent returns at identical confidence levels. Moreover, the GED-GARCH model can estimate the downside dynamic VaR accurately for WTI and Brent oil returns.     

The Effects of Foreign Currency Derivatives on the Monetary Policy Exchange Rate Channel in China

This paper examines changes in the monetary policy exchange rate channel in the presence of foreign currency derivatives (FCD) markets in China. Initially a theoretical macroeconomics model incorporating the exchange rate risk hedging is presented, and this is followed by an empirical test. A theoretical model implies that with more firms using foreign currency derivatives to hedge the exchange rate risk, the effect of the exchange rate on the net exports will be weaker and may even be reversed. The empirical section uses Structure Vector Autoregression (SVAR) models with China's monthly macro data over the 2000–2013 period to assess the impact of the FCD market on the exchange rate channel. Empirical support for the changes in the exchange rate channel transmission is found. By impulse response function (IRF) analysis, with the emergence of the domestic FCD market in China, in the long run the probability becomes higher that the negative effect of RMB appreciation on China's net exports to the US is reversed; meanwhile the negative effects of RMB appreciation on the overall net exports and the net exports to the EU become gradually weaker on average.     

Capital Market Integration in Euroland: The Role of Banks

The introduction of the euro marks a milestone in the process of European financial market integration. This paper analyzes the implications of the euro for cross-border banking activities. A portfolio model is used which captures the role of banks as providers of informational and of risk-diversification services. By eliminating exchange rate risks, the euro enhances the incentives of banks to expand within Euroland. Yet, while the currency bias in bank portfolios will be eliminated, the home bias will remain. Implications of market integration for the risk-taking and the monitoring of banks are not clear-cut.