An empirical investigation of multiperiod tail risk forecasting models

In the context of multiperiod tail risk (i.e., VaR and ES) forecasting, we provide a new semiparametric risk model constructed based on the forward-looking return moments estimated by the stochastic volatility model with price jumps and the Cornish–Fisher expansion method, denoted by SVJCF. We apply the proposed SVJCF model to make multiperiod ahead tail risk forecasts over multiple forecast horizons for S&P 500 index, individual stocks and other representative financial instruments. The model performance of SVJCF is compared with other classical multiperiod risk forecasting models via various backtesting methods. The empirical results suggest that SVJCF is a valid alternative multiperiod tail risk measurement; in addition, the tail risk generated by the SVJCF model is more stable and thus should be favored by risk managers and regulatory authorities.     

Decomposing the VIX: Implications for the predictability of stock returns

The VIX index is not only a volatility index but also a polynomial combination of all possible higher moments in market return distribution under the risk-neutral measure. This paper formulates the VIX as a linear decomposition of four fundamentally different elements: the realized variance (RV), the variance risk premium (VRP), the realized tail (RT), and the tail risk premium (TRP), respectively. Using an innovative and nonparametric tail risk measure, we find that approximately one-third of the VIX's formation is attributed to the TRP. In addition to VRP, RT and TRP are crucial components for predicting future returns on equity portfolios.     

极端风险事件下股票市场与公司债券市场的尾部风险溢出研究——基于MVMQ-CAViaR模型

构建MVMQ-CAViaR模型,结合金融市场内部极端风险事件和外部极端风险事件,考量股票市场与公司债券市场的尾部风险溢出问题。结果表明,在金融市场内部极端风险事件下,股灾期间仅存在股票市场对公司债券市场单向的尾部风险溢出。公司债券违约潮期间,股票市场与公司债券市场之间存在双向不对称的尾部风险溢出,且公司债券市场对股票市...     

Constant Proportion Debt Obligations (CPDOs): modeling and risk analysis

Constant Proportion Debt Obligations (CPDOs) are structured credit derivatives that generate high coupon payments by dynamically leveraging a position in an underlying portfolio of investment-grade index default swaps. CPDO coupons and principal notes received high initial credit ratings from the major rating agencies, based on complex models for the joint transition of ratings and spreads for all names in the underlying portfolio. We propose a parsimonious model for analysing the performance of CPDO strategies using a top-down approach that captures the essential risk factors of the CPDO. Our approach allows us to compute default probabilities, loss distributions and other tail risk measures for the CPDO strategy and analyse the dependence of these risk measures on various parameters describing the risk factors. We find that the probability of the CPDO defaulting on its coupon payments can be made arbitrarily small—and thus the credit rating arbitrarily high—by increasing leverage, but the ratings obtained strongly depend on assumptions on the credit environment (high spread or low spread). More importantly, CPDO loss distributions are found to exhibit a wide range of tail risk measures inside a given rating category, suggesting that credit ratings are insufficient performance indicators for such complex leveraged strategies. A worst-case scenario analysis indicates that CPDO strategies have a high exposure to persistent spread-widening scenarios and that CPDO ratings are shown to be quite unstable during the lifetime of the strategy.     

Shedding light on a dark matter: Jump diffusion and option-implied investor preferences

We compare equilibrium jump diffusion option prices with endogenously determined stochastic dominance (SD) option bounds. We use model parameters from earlier studies and find that most equilibrium model prices consistent with SD bounds yield economically meaningless results. Further, the implied distributions of the SD bounds exhibit a tail risk comparable to that of the underlying return data, thus shedding light on the dark matter of the inconsistency of physical and risk-neutral tail probabilities. Since the SD bound assumptions are weaker, we conclude that these bounds should either replace or be used to verify the equilibrium model results.     

Environmental,social, and governance practices and perceived tail risk

Using the implied volatility smirk on individual equity securities to measure perceived tail risk, we find that better environmental, social and governance (ESG) practices significantly reduce ex-ante expectations of a left-tail event. Our findings are robust to using multiple model specifications and to adjusting for potential endogeneity concerns. We also show that, while practices in each ESG pillar are important in reducing perceived tail risk, the environmental pillar plays the most important role. Our results indicate that investors consider strong ESG practices to be insurance against left-tail events rather than wasteful investment borne out of managers’ own values or self-interest.     

Trapped in diversification – another look at the risk of fund of hedge funds

Recent literature implies that despite being more diversified, fund of hedge funds (FOFs) are exposed to tail risk. We propose an explanation for this phenomenon; tail risk is a systematic risk factor for hedge funds, which by construction, explains the higher portion of the returns in the diversified portfolios. Our study suggests that not only an additional tail risk factor improves the explanatory power of the factor model, the relative importance of tail risk factor increases with the number of underlying hedge funds in an FOF portfolio. Furthermore, we demonstrate that FOFs with a short history, higher management fees, leverage and requiring shorter lockup periods are more sensitive to tail risk.     

基于拓扑数据模型的车险操作风险度量

以机动车辆保险为研究对象,分析车险核心业务流程中操作风险的表现形式,借助拓扑数据模型及Monte Carlo模拟对其风险进行度量。结果显示:损失强度表现出较强的厚尾性,事件频率具有高频性,但总损失额分布的厚尾特征不明显,这些结果为操作风险进行经济资本配置及管理提供了依据。     

Extremes on the discounted aggregate claims in a time dependent risk model

This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables (rv's). Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed rv's. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims. A simulation study is performed in order to validate the results obtained in the free interest risk model.     

Asymptotic ruin probabilities for a discrete-time risk model with dependent insurance and financial risks

This contribution focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account and they are equipped with a wide type of dependence structure. We derive precise asymptotic formulas for the ruin probabilities when the insurance risk has a dominatedly varying tail. In the special case of regular variation, the corresponding formula is proved to be uniform for the time horizon.     

Tail risk of coal futures in China's market

This study evaluates the downside tail risk of coal futures contracts (coke, coking coal and thermal coal) traded in the Chinese market between 2011 and 2021, measured by value at risk (VaR). We examine the one-day-ahead VaR forecasting performance with a hybrid econometric and deep learning model (GARCH-LSTM), GARCH family models, extreme value theory models, quantile regression models and two naïve models (historical simulation and exponentially weighted moving average). We use four backtesting techniques and the model confidence set to identify the optimal models. The results suggest that the models focusing on tail risk or utilising long short-term memory generate more effective risk management.     

Risk management under extreme events

This article presents two applications of extreme value theory (EVT) to financial markets: computation of value at risk (VaR) and cross-section dependence of extreme returns (i.e., tail dependence). We use a sample comprised of the United States, Europe, Asia, and Latin America. Our main findings are the following. First, on average, EVT gives the most accurate estimate of VaR. Second, tail dependence of paired returns decreases substantially when both heteroscedasticity and serial correlation are filtered out by a multivariate GARCH model. Both findings are in agreement with previous research in this area for other financial markets.     

宏微观分析相结合的信贷风险预测模型研究

我国现有的信贷风险评估方法存在宏微观分析结合不紧密以及风险评估不全面的问题.本文在基于财务分析的企业风险评估模型基础上,构建了宏微观分析相结合的信贷风险预测模型.建模的主要工作包括:选择反映行业信贷风险的指标与反映宏观经济变化的指标;确定反映宏观经济变化的指标与反映行业信贷风险指标之间的函数关系;依据以上的关联函数和宏观经济指标预测值,计算行业信贷风险调整系数;据此对属于该行业的企业即期信贷风险指标进行调整,对企业的信贷风险进行前瞻性预测.作者还利用证券市场数据检验了上述模型的准确性,结果表明模型可以有效预测企业未来的信贷风险.     

Measuring tail thickness under GARCH and an application to extreme exchange rate changes

Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including generalized autoregressive conditional heteroskedastic (GARCH) models and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail thickness due to small sample bias. Thus, high quantile estimation may lead to a substantial underestimation of tail risk.     

The extreme risk connectedness of the new financial system: European evidence

The paper empirically analyses the tail risk connectedness between FinTech and the banking sector in the European context over 2015–2022. For this purpose, we use the Tail-Event driven NETworks (TENET) risk model, i.e., we can capture the behaviour of extreme (negative and positive) risk spillover within the financial system. The results highlight how most tail risk spillovers are from banks to FinTech firms. Also, the findings suggest that the spillovers of cross-sector tail risk are more significant in downside (bearish) risk conditions than in upside (bullish) one. We find evidence of an asymmetric effect of extreme risk spillover to the real economy. Finally, we evaluate the monetary policy’s impact on extreme risk. Our findings highlight the importance of closer monitoring risk spillover between FinTech institutions and the European banking system to maintain financial stability.     

From me to you: Measuring connectedness between Eurozone financial institutions

This paper aims to analyse the tail risk spillover between banks, insurance companies and the shadow banking system in the Eurozone contest. These intra-sectoral interdependencies between financial market participants have contributed to the spread of instability in the financial system. Therefore mapping these links is important for policy-makers to provide supervisory tools and can be a key input into the design of macroprudential policies. For this purpose, we adopt the Tail-Event driven NETwork (TENET) risk model. The TENET is a useful method to map the tail interconnection between the three sectors and to provide systemic risk measures that take into account the “too big to fail” and “too big to interconnected” concepts. The results suggest that each financial sector has a significant impact on the other. By comparing the contribution of each sector, we show that banks are the largest emitters of risk. However, also shadow banking firms are systemic important, given their high level of connection. The work provides a clear view of risk spillovers and interconnection dynamics during the crisis providing a meaningful ranking of the systemic important financial institutions.     

巨灾风险厚尾分布：POT模型及其应用

针对Gamma,LognormM和Weibull等传统厚尾分布拟合巨灾风险的不足,本文一方面从理论上分析探讨了POT模型及其拟合巨灾厚尾风险的相对优势,另一方面应用POT模型和GPD分布,对我国1952年～2008年间地震直接经济损失数据进行拟合,发现了POT模型拟合巨灾风险厚尾部分的效果比Gamma、LognormM...     

Probability weighting functions implied in options prices

The empirical pricing kernels estimated from index options are non-monotone (Rosenberg and Engle, 2002, Bakshi et al., 2010) and the corresponding risk-aversion functions can be negative (Aït-Sahalia and Lo, 2000, Jackwerth, 2000). We show theoretically that these and several other properties of empirical pricing kernels are consistent with rank-dependent utility model with probability weighting function, which overweights tail events. We also estimate the pricing kernels nonparametrically from the Standard & Poor's 500 index options and construct empirical probability weighting functions. The estimated probability weights typically have the inverse-S shape, which overweights tail events and is widely supported by the experimental decision theory.     

Fast simulations in credit risk

We consider the problem of simulating tail loss probabilities and expected losses conditioned on exceeding a large threshold (expected shortfall) for credit portfolios. Our new idea, called the geometric shortcut, allows an efficient simulation for the case of independent obligors. It is even possible to show that, when the average default probability tends to zero, its asymptotic efficiency is higher than that of the naive algorithm. The geometric shortcut is also useful for models with dependent obligors and can be used for dependence structures modeled with arbitrary copulae. The paper contains the details for simulating the risk of the normal copula credit risk model by combining outer importance sampling with the geometric shortcut. Numerical results show that the new method is efficient in assessing tail loss probabilities and expected shortfall for credit risk portfolios. The new method outperforms all known methods, especially for credit portfolios consisting of weakly correlated obligors and for evaluating the tail loss probabilities at many thresholds in a single simulation run.     

Long-term asset tail risks in developed and emerging markets

A power law typically governs the tail decay of financial returns but the constancy of the so-called tail index which dictates the tail decay remains relatively unexplored. We study the finite sample properties of some recently proposed endogenous tests for structural change in the tail index. Given that the finite sample critical values strongly depend on the tail parameters of the return distribution we propose a bootstrap-based version of the structural change test. Our empirical application spans developed and emerging financial asset returns. Somewhat surprisingly, emerging stock market tails are not more inclined to structural change than their developed counterparts. Emerging currency tails, on the contrary, do exhibit structural shifts in contrast to developed currencies. Our results suggest that extreme value theory (EVT) applications in hedging tail risks can assume stationary tail behavior over long time spans provided one considers portfolios that solely consist of stocks or bonds.