We present in this article a non-parametric value-at-risk (VaR+CVaR) algorithm that remains accurate for an arbitrarily large number of underlying positions. The algorithm solves the two inherent problems of VaR estimation. First, past history is not directly applicable to the future, but all predictions of the future are based on the past. Second, VaR estimation is equivalent to modeling a single corner of a high-dimensional space (the corner where all bets lose simultaneously). The algorithm only uses mathematical methods that strictly do not degrade in accuracy at high-dimensions. Historical data are then directly incorporated with all high-dimensional relationships present, without manipulation. We test the algorithm with an ensemble of 500 portfolios with random positions across 49 distinct liquid futures of different expiries (VIX, equity indexes, gov. bonds, rates, energy, metals, livestock, agriculture, and softs). All VaR estimations are performed strictly blind to the future. The median portfolio rate of loss exceeding the 99
In this paper, we use a Markov regime-switching model to analyze hedge fund performance in China, distinguishing between economic expansion and recession phases, and we employ a stepwise regression method to identify the key factors influencing hedge fund strategies within each economic regime. This model adeptly captures the nonlinear characteristics of hedge fund returns, allowing for a precise assessment of performance fluctuations tied to different economic states. Our findings reveal that during economic expansions most hedge funds struggle to generate significant positive alpha and rely primarily on momentum strategies. However, during recessions, hedge funds strategically reduce their risk exposure, with neutral, event-driven, arbitrage and bond strategies, for example, showing the ability to generate positive alpha returns. This shift in risk exposure and asset allocation underscores the adaptive strategies used by hedge funds to mitigate risks and capitalize on opportunities during downturns. This study provides a comprehensive analysis of hedge fund performance in China, a rapidly evolving financial market that presents unique challenges and opportunities distinct from more developed Western markets.
We develop an innovative application of Kelly et al's 2018 instrumented principal component analysis model, wherein regression-based exposures (betas) to risk factors are used as characteristics. We show that this new type of model, which hybridizes elements from cross-sectional, statistical and time series models, has many advantages. It inherits the high precision and depth of analysis typically found in cross-sectional models, while dramatically reducing their data requirements. In addition, it is precise, allows the inclusion of many characteristics while remaining numerically stable, and greatly simplifies the construction of multiregional models. Finally, although calibrated using a universe of funds, this model has excellent precision and low bias when used to analyze and optimize portfolios of stocks.
This paper investigates Chinese climate policy uncertainty (CCPU) as a systematic risk factor within the intertemporal capital asset pricing model framework. We establish that CCPU carries a significantly negative risk premium in the cross section of Chinese stock returns. Industry exposure analysis reveals the economic mechanism underpinning this result: assets with positive CCPU betas, predominantly in green sectors, serve as hedges against deteriorations in the investment opportunity set. Further, we demonstrate that rising CCPU predicts lower future aggregate market returns and higher volatility, signaling deteriorating investment conditions. This predictive power fundamentally explains the observed negative premium, as investors accept lower returns for holding hedging assets that provide protection against CCPU.
Stochastic volatility models are employed to measure and manage financial risks in cryptocurrency markets. In this study, a subordinated Levy process, driven by a univariate integrated square-root Cox-Ingersoll-Ross process is examined. The resulting stochastic volatility normal tempered stable (SVNTS) process effectively captures key stylized facts such as heavy tails, asymmetry and volatility clustering. Leveraging the fast Fourier transform (FFT), a numerical approximation of the return probability density is derived, facilitating the computation of tail risk measures. The SVNTS model is calibrated to a range of cryptocurrency data sets, with its goodness-of-fit rigorously evaluated. In addition, a novel parameter estimation framework is proposed for the SVNTS distribution. This approach integrates maximum likelihood estimation based on the FFT-derived density, augmented by a Bayesian optimization scheme employing Gaussian regression and expected improvement for initial parameter selection. Final refinement is achieved through particle swarm optimization, a technique rarely used in comparable studies. To capture the intricate dependencies among assets, a Student t-copula is employed, enabling the separation of marginal distributions from their joint dependency structure. This distinction is essential for accurately modeling tail dependence, particularly under conditions of market stress. Based on a robust multivariate simulation framework, portfolio optimization is performed by minimizing conditional value-at-risk across a selection of cryptocurrencies. Finally, the accuracy of the resulting value-at-risk and conditional value-at-risk estimates is validated through extensive backtesting procedures.
For a static model of n individuals generated by heavy-tailed losses, under the assumption that there exist asymptotic independence and dependence structures between the losses, we derive asymptotic formulas for both the systemic expected shortfall and marginal expected shortfall based on higher-moment capital allocation rules. Our results indicate that systemic risk is asymptotically proportional to the value-at-risk of a representative random variable, and it is influenced by the risk aversion parameter p and the structure of asymptotic dependence, while the structure of asymptotic independence has a negligible effect. In addition, simulation studies are conducted to better illustrate our results.
Accurately predicting extreme tail risk is crucial for China's banking sector. However, the need for long time series in order to capture extreme events introduces nonstationarity to financial data, posing significant challenges to traditional volatility models, which assume stationarity. Further, the limited availability of extreme tail data can result in unstable estimates, complicating the risk assessment process. To address these issues, we propose the component GARCH-MIDAS-EVT-X model: a model to forecast extreme value-at-risk (VaR) and expected shortfall (ES) that combines generalized autoregressive conditional heteroscedasticity (GARCH), mixed data sampling (MIDAS), extreme value theory (EVT) and economic covariates X. The component GARCH-MIDAS volatility model surpasses conventional GARCH approaches by effectively capturing dynamic changes in both conditional and unconditional variance, as is essential for accurately modeling the complex and evolving volatility of China's banking sector. In addition, the integration of EVT addresses the challenge of data scarcity for extreme events. We apply our model to a stock index representing China's banking sector and employ a comprehensive set of backtesting methods for VaR and ES. The results demonstrate that our model outperforms other competing models, underscoring its effectiveness in forecasting extreme risks. This study demonstrates the effectiveness of combining component GARCH-MIDAS and EVT methodologies, offering a substantial contribution to extreme risk prediction in the context of China's banking sector.
This paper applies the semiparametric generalized autoregressive conditional heteroscedasticity (GARCH) models to calculate value-at-risk (VaR) and expected shortfall (ES) based on an object-driven smoothing approach. In the first stage, the scale function is estimated with numerous given bandwidths, and different GARCH models are fitted to the descaled returns. Suitable models are then filtered using different backtesting methods, including a recent traffic light approach for backtesting the ES. A new loss function for a firm's ES is introduced and used as the main object function for selecting the best model in the final stage. Empirical applications demonstrate that the proposed procedure effectively identifies models with good out-of-sample performance for VaR and ES forecasting. Moreover, the proposed object-driven smoothing procedure is applicable to other research areas.
It is well known that high-frequency traders frequently use low-latency trading algorithms to submit and cancel orders at superhuman speeds. Our study demonstrates that high-frequency traders cancel many trading orders within 20 milliseconds of submission, engaging in anticipatory trading and creating arbitrage opportunities in the E-mini S&P 500 and the SPDR S&P 500 ETF Trust, which enables them to earn significant profits after transaction costs. Moreover, market participants lacking latency and sophisticated trading algorithms will likely encounter higher execution costs. As a practical policy measure, we propose implementing batch auctions, which will mitigate queuing risk for high-frequency traders and yield beneficial consequences for market quality.
We conduct a comparative analysis of quantitative models for assessing risk contagion and systemic risk within the Chinese financial market, focusing on four key methodologies: vector autoregression-forecast error variance decomposition (VAR-FEVD), quantile vector autoregression-forecast error variance decomposition (QVAR-FEVD), linear conditional value-at-risk (CoVaR) and tail-event driven network (TENET). Our analysis underscores the significance of network construction methods in accurately depicting the spillover effects among financial institutions. The research delves into the performance of financial networks by comparing "physical" networks, evaluating predefined networks within the dynamic network quantile regression model, and identifying systemically important financial institutions across various network configurations. In particular, the TENET model emerges as particularly adept, outperforming the other models in capturing both mean and tail risk spillovers. This paper not only deepens the understanding of systemic risk in China but also provides valuable recommendations for policy makers to design effective regulatory frameworks to mitigate potential crises.
This paper examines the application of various stochastic volatility models to real data and demonstrates their effectiveness in calibrating a wide range of options, including those with short-term maturities during normal conditions and during the distressed market conditions of the Covid-19 pandemic. The analysis reveals that Heston's 1993 model encounters challenges in accurately fitting the short-term smile and skew of volatility surfaces in the Standard & Poor's 500 option market. To address these limitations, we investigate advanced volatility models that capture the market's "rough" behavior, albeit with higher computational demands. Further, we incorporate a neural network into the calibration process for these models and show that this scheme enables a significant speedup. In particular, we demonstrate that this pattern allows us to incorporate non-Markovian components and fractional Brownian motion, which increases the modeling capabilities and gives a more realistic representation of markets. We propose an alternative model that combines stochastic elements with local volatility through Monte Carlo simulations, theoretically allowing for a perfect fit. However, this method proves to be computationally demanding and impractical for real-world applications. Our observations indicate that the overall fit of the selected models remains robust with regard to calibration accuracy, even during the Covid-19 market shock and in the presence of rapid interest rate hikes. However, the Heston model exhibits higher parameter fluctuations when the forward yield curve steepens and interest rates increase. Moreover, we find that the main drawbacks of stochastic volatility models are their inability to effectively model persistently high implied volatility and accurately capture event-driven skews in the volatility surface.
We propose a new semi-analytical pricing model for Bermudan swaptions based on swap-rate distributions and the correlations between them. The model does not require product-specific calibration.
We examine whether differences in the tone of verbal communications by the central bankers of the European Central Bank and those of central banks in the euro area can impact investors' willingness to invest in euro area small- to medium-sized enterprises. Our measure of diverging communication tone is constructed using textual analysis and defined as the distance between the tones of the speeches of the respective central bankers. We use confidential firm-level data to show that a greater divergence in the tone of communication decreases investors' willingness to invest.
This study presents a method-of-moments copula approach in a dynamic setting for estimating the market risk of asset portfolios. On using exponential generalized conditional heteroscedasticity (EGARCH) volatility-adjusted returns to account for heteroscedasticity, our findings reveal that the method-of-moments approach significantly reduces the copula estimation time for 99% value-at-risk estimates without loss of accuracy while outperforming several benchmark models. This creates an advantage for practical applications, especially for portfolios with higher dimensions. We also use this model to calculate 97.5% expected shortfall estimates. Our empirical results are based on a mixed 21-dimensional portfolio consisting of five classes of financial assets often included in trading books of financial institutions (stocks, stock indexes, bonds, foreign exchange and commodities). An investigation period of nearly 35 years (January 1990 to November 2024) ensures the inclusion of several severe crisis periods with strong sudden price movements and corresponding shocks to the dependence structure. More than 8200 trading days and a rolling 250-day estimation window for dynamic out-of-sample risk estimates generate an interesting base for accuracy tests. Overall, the best accuracy is generated by a meta-Student t model using EGARCH volatility-adjusted returns with method-of-moments copula estimation. An additional simulation study shows that the computational advantage of our dynamic method-of-moments copula approach persists for portfolios of higher dimensions with up to 400 risk factors.
This paper evaluates the method of naive risk parity (RP) in portfolio trading, particularly with Standard & Poor's 500 stocks as components. Several sample selection criteria based on prevalent risk factors are applied, and the dynamic technique of RP is examined. Three performance risk-adjusted ratios and four downside risk measurements are used for evaluation. It is found that both conventional and dynamic versions of RP portfolios generally outperform traditional value-weighted and equal-weighted portfolios. In particular, when firm size is used as a sample selection criterion, RP portfolios show the largest improvements compared with other portfolio types. Various combinations of formation and holding periods are investigated, and the empirical results for subperiods are produced and discussed. When the economy is in a downturn, RP portfolios with a selection criterion based on stock momentum outperform other strategies, presumably due to volatilities among the stocks being highly correlated. This paper sheds light on the application of the RP strategy with components only from stocks, and it shows that for investments with a long horizon, RP constitutes an effective and profitable alternative risk-adjusted strategy.
