Conditional Copula Models Research Articles

Semiparametric copula models applied to the decomposition of claim amounts

In this paper, we develop a conditional copula model to analyze the distribution of a claim that generates different types of costs and/or simultaneously impacts several guarantees. Our methodology is adapted to taking into account the particular structure of our data, since observations are subject to right-censoring. Right-censoring occurs since payment of a claim is not made instantaneously, and therefore unsettled claims only provide a partial information on the phenomenon that one wishes to model. The new methodology that we develop is supported by theoretical results that show the asymptotic normality of our estimators. A simulation study and a real data analysis illustrate the method.

A wavelet regression approach to dependence calibration in conditional copula model

A wavelet regression approach to dependence calibration in conditional copula model

A conditional copula model to identify the response of runoff probability to climatic factors

Understanding the response of runoff to climate drivers is important to ensure rational water allocation and address the risk of drought. Many models that assess the effect of climate factors on the response of runoff volume have been developed and widely used. However, models that assess the response of the probability of runoff occurrence (runoff probability) are lacking. In this study, we developed a model by integrating a conditional probability distribution (CPD) and a copula function model to assess the effect of climate conditions on variation of the probability of runoff occurrence. The developed model was applied to the basin of Poyang Lake, the largest freshwater lake in China. The study showed that Frank copula was the copula that had the best-fitted effect to identify the impact of climate factors (except for precipitation and air temperature [AT] in low flow period [LFP]) on the probability of runoff occurrence. The copulas with the best-fitted effect of precipitation and AT is the Gumbel copula and Clayton copula during LFP, respectively. Precipitation, relative humidity (RH), and water vapor pressure (WP) were positive with streamflow variation, while wind speed (WS), potential evapotranspiration (ET0), and sunshine duration (SD) were negative with runoff, but AT had an inverse relation with the streamflow during high flow period (HFP) and LFP. Sensitivity analysis indicated that precipitation has a weaker effect on the likelihood of extreme hydrological events than many other climate factors (such as RH and SD). Moreover, the sensitivity of runoff probability to climatic factors tended to be relatively stable during HFP, which was in contrast to that during LFP. This research highlights the significance of considering change conditions when evaluating runoff response to climate drivers, which is consistent with the objective of achieving more accurate runoff predictions to combat climate change and extreme weather conditions.

Conditional copula models for correlated survival endpoints: Individual patient data meta-analysis of randomized controlled trials.

Correlations among survival endpoints are important for exploring surrogate endpoints of the true endpoint. With a valid surrogate endpoint tightly correlated with the true endpoint, the efficacy of a new drug/treatment can be measurable on it. However, the existing methods for measuring correlation between two endpoints impose an invalid assumption: correlation structure is constant across different treatment arms. In this article, we reconsider the definition of Kendall's concordance measure (tau) in the context of individual patient data meta-analyses of randomized controlled trials. According to our new definition of Kendall's tau, its value depends on the treatment arms. We then suggest extending the existing copula (and frailty) models so that their Kendall's tau can vary across treatment arms. Our newly proposed model, a joint frailty-conditional copula model, is the implementation of the new definition of Kendall's tau in meta-analyses. In order to facilitate our approach, we develop an original R function condCox.reg(.) and make it available in the R package joint.Cox (https://CRAN.R-project.org/package=joint.Cox). We apply the proposed method to a gastric cancer dataset (3288 patients in 14 randomized trials from the GASTRIC group). This data analysis concludes that Kendall's tau has different values between the surgical treatment arm and the adjuvant chemotherapy arm (p-value<0.001), whereas disease-free survival remains a valid surrogate at individual level for overall survival in these trials.

Omnibus test for covariate effects in conditional copula models

Conditional copulas describe the conditional dependence and the influence that covariates have on the dependence structure between two (or more) variables. Of interest is to test the null hypothesis that the covariates have a specific effect. This paper proposes an omnibus test for testing the null hypothesis of a specified effect of the covariates. The test statistic is designed for having power against many alternatives, and can be used to test for a variety of covariate effects (no effects, linear effects, partial effects, etc.). A special case is the testing problem that the covariates do not affect the dependence structure. In this semiparametric framework the marginal distribution functions are estimated using nonparametric kernel techniques and the parametric dependence model is estimated using maximum likelihood estimation. We establish the asymptotic distribution of the test statistic under the null hypothesis, and evaluate the finite-sample performance of the test via a simulation study, which also includes comparisons with alternative tests. A real data analysis illustrates the practical use of the test.

Reflection of government performance from foreign exchange market through engineered mechanism using conditional copula model

This paper investigates governments’ performance in the country. We achieved this objective differently. We employed an inverse method of assessment, with the utilization of factor copula modeling technique, to study the dependence relationship of exchange rates returns as auxiliary variables, the performance of political and army government tenures in the country in the last two decades are evaluated. Through factor analysis, common factors for the exchange rate are obtained. The analysis shows that conditioned on the common factors, the dependence amongst the elected currencies are strongly asymmetric in most of the tenures except the term of Pakistan Muslim League-Nawaz, and condition on common factor Clayton copula demonstrating hypothesis is more suitable. However, we perceive high left tail reliance among foreign currency returns during Pakistan Muslim League-Nawaz tenure, and the condition on common factor Gumbel copula molding assumption is more appropriate. We are signifying the foulest government performance in the country among all occupancies under consideration.

Dynamic Dependence Structure between Chinese Stock Market Returns and RMB Exchange Rates

ABSTRACT This paper investigates the dynamic dependence structure between the Chinese stock market and the real exchange rate of the Chinese renminbi (RMB) with unconditional and conditional copula models for the period July 22, 2005, to December 31, 2017. The results show that the crisis induced significant structural breaks, and the relationship is weak before the global financial crisis but substantially stronger after the financial crisis, regardless of whether the correlation is positive or negative. Our findings have important implications for global portfolio diversification, risk management, and China’s exchange rate policy.

Bayesian inference for conditional copulas using Gaussian Process single index models

Parametric conditional copula models allow the copula parameters to vary with a set of covariates according to an unknown calibration function. Flexible Bayesian inference for the calibration function of a bivariate conditional copula is introduced. The prior distribution over the set of smooth calibration functions is built using a sparse Gaussian process (GP) prior for the single index model (SIM). The estimation of parameters from the marginal distributions and the calibration function is done jointly via Markov Chain Monte Carlo sampling from the full posterior distribution. A new Conditional Cross Validated Pseudo-Marginal (CCVML) criterion is used to perform copula selection and is modified using a permutation-based procedure to assess data support for the simplifying assumption. The performance of the estimation method and model selection criteria is studied via a series of simulations using correct and misspecified models with Clayton, Frank and Gaussian copulas and a numerical application involving red wine features.

What drives flight to quality?

AbstractThe returns of equities and bonds tend to be positively correlated, but in extreme situations this relation reverses. Large negative equity returns co‐occur with large positive bond returns. This is potentially caused by investors reassessing their risk preferences and shifting their wealth to less risky asset classes, which is frequently termed flight to quality. We examine macroeconomic factors to identify the driving variables using a conditional copula model. Analysing quarterly data from 1952 to 2014, we find that the Treasury bill rate is the most significant driver. This insight is useful for asset allocation and risk management.

Measuring crisis risk using conditional copulas: An empirical analysis of the 2008 shipping crisis

SummaryThe shipping crisis starting in 2008 was characterized by sharply decreasing freight rates and sharply increasing financing costs. We analyze the dependence structure of these two risk factors employing a conditional copula model. As conditioning factors we use the supply and demand of seaborne transportation. We find that crisis risk strongly increased already about 1 year before the actual crisis outburst and that the shipping crisis was predominantly driven by an oversupply of transport capacity. Therefore, market participants could have prevented or alleviated the consequences of the crisis by reducing the ordering and financing of new vessels.

Default Risk of Mortgage Credits for Lenders

This paper applies a conditional copula model to investigate the dependence structure of house prices and default rates by analyzing their extreme dependence in order to quantify the default risk of mortgage credits for lenders. Therefore, we use housing supply factors and economic factors as well as interest rates and mortgage loan-to-price ratios as explaining variables. Examining quarterly data from 1985 to 2015 we find that new housing units starts, the existing mortgage loan-to-price ratio as well as the home mortgage loan-to-price ratio can be used to quantify the default risk of mortgage credits for lenders.

Conditional copula models for right-censored clustered event time data.

This article proposes a modeling strategy to infer the impact of a covariate on the dependence structure of right-censored clustered event time data. The joint survival function of the event times is modeled using a conditional copula whose parameter depends on a cluster-level covariate in a functional way. We use a local likelihood approach to estimate the form of the copula parameter and outline a generalized likelihood ratio-type test strategy to formally test its constancy. A bootstrap procedure is employed to obtain an approximate $p$-value for the test. The performance of the proposed estimation and testing methods is evaluated in simulations under different rates of right-censoring and for various parametric copula families, considering both parametrically and nonparametrically estimated margins. We apply the methods to data from the Diabetic Retinopathy Study to assess the impact of age at diabetes onset on the time to loss of visual acuity.

Diversification into Emerging Markets - An Australian and the US Perspective Using a Time-varying Approach

Over the past two decades, a number of studies have examined the benefits of diversifying equity investments internationally, particularly into emerging markets. In the portfolio construction process, many researchers have criticised Markowitz's Portfolio Theory because of its inherent assumptions such as symmetric and constant correlations. In this study, we use a conditional copula model to estimate the time-varying asymmetric correlations of stock markets and construct optimal portfolios by using estimated correlations. We find that optimised portfolios provide significant benefits for both Australian and the US investors. Out-of-sample results show Copula model provides results closer to the in-sample-estimated benefits of diversification. The results have important implications for portfolio managers who seek to diversify into emerging markets.

Stock Market Integration in China: Evidence from the Asymmetric DCC Model and Copula Approach

We investigate the dynamic dependence structure between the daily stock returns of the A and B shares of the Shanghai and Shenzhen stock markets in China, using time-varying conditional copula and asymmetric dynamic conditional correlation models. We find that the Shanghai market’s A and B shares are more integrated than those of the Shenzhen market. Further, the dynamic dependences between the shares for both markets are asymmetric and lower-tailed, and an increasing correlation with the opening up of the B shares market to Chinese citizens around 2001 is evident.

The Shipping Crisis Starting in 2008: Could It Have Been Avoided?

The shipping crisis starting in 2008 was characterized by sharply decreasing freight rates and sharply increasing financing costs. This led to numerous insolvencies of shipping companies and impairment losses of their lending institutions. We analyze the dependence structure of these two risk factors employing a conditional copula model with a focus on time-varying tail dependence, which we interpret as shipping crisis risk. As conditioning factors we use the supply and demand of seaborne transportation. We find that crisis risk strongly increased already about one year before the actual outburst of the crisis. Our results also show that the shipping crisis was predominantly driven by an oversupply of transport capacity rather than a declining demand. Taken these results together, market participants could have avoided or alleviated the crisis' consequences by reducing the ordering and financing of new vessels.

A development of downscaling scheme for sub-daily extreme precipitation using conditional copula model

A development of downscaling scheme for sub-daily extreme precipitation using conditional copula model

Sparse conditional copula models for structured output regression

We deal with the multiple output regression task where the central theme is to capture the sparse output correlation among the output variables. Sparse inverse covariance learning of linear Gaussian conditional models has been recently studied, shown to achieve superb prediction performance. However, it can fail when the underlying true input–output process is non-Gaussian and/or non-linear. We introduce a novel sparse conditional copula model to represent the joint density of the output variables. By incorporating a Gaussian copula function, yet modeling univariate marginal densities by (non-Gaussian) mixtures of experts, we achieve high flexibility in representation that admits non-linear and non-Gaussian densities. We then propose a sparse learning method for this copula-based model that effectively imposes sparsity in the conditional dependency among output variables. The learning optimization is efficient as it can be decomposed into gradient-descent marginal density estimation and the sparse inverse covariance learning for the copula function. Improved performance of the proposed approach is demonstrated on several interesting image/vision tasks with high dimensions.

Modeling the Dependence Structure between Australian Equity and Real Estate Markets – A Copula Approach

In the last decade, the Australian market for Real Estate Investment Trusts (REITS) has shown substantial growth rates. Australian Real Estate Investment Trusts (AREITS) are a unitized portfolio of property assets which allows investors to purchase a share in a diversified and professionally managed portfolio of real estate. We apply conditional copula models in order to investigate the dependence structure between returns of AREITS and Australian equity markets. The dynamic analysis is based on an AR-GARCH approach to model time-varying volatility of the individual series in combination with different copulas to capture the dependence structure between the standardized residuals. The Gaussian, Student t, Clayton and Gumbel copula are fitted and so-called ‘blanket’ goodness-of-fit tests are conducted in order to examine the appropriateness of the different copula functions. We also compare the suggested copula models to a standard variance-covariance approach and the Dynamic Conditional Correlation (DCC) model. We find significant positive correlation between the series what somehow contradicts earlier studies on the topic finding negative or only weak positive correlations between REITS and equity investments. Therefore, for Australian markets the diversification potential of investments in REITS might be less significant than for overseas markets. We also find significant tail dependence, in particular in the tail dependence structure that is best modelled by the Student t copula. Conducting a back-testing Value-at-Risk study for a portfolio combining investments in real estate and equity we find that the conditional copula as well as the DCC model significantly outperforms a static variance covariance approach. Our findings suggest that ignoring the complex and dynamic dependence structure in favour of a simple multivariate normal model leads to a significant underestimation of the actual risk.

Modelling the Dependence Structure between Australian Equity and Real Estate Markets – a Copula Approach

In the last decade, the Australian market for Real Estate Investment Trusts (REITS) has shown substantial growth rates. Australian Real Estate Investment Trusts (AREITS) are a unitized portfolio of property assets which allows investors to purchase a share in a diversified and professionally managed portfolio of real estate. We apply conditional copula models in order to investigate the dependence structure between returns of AREITS and Australian equity markets. The dynamic analysis is based on an AR-GARCH approach to model time-varying volatility of the individual series in combination with different copulas to capture the dependence structure between the standardized residuals. The Gaussian, Student t, Clayton and Gumbel copula are fitted and so-called ‘blanket’ goodness-of-fit tests are conducted in order to examine the appropriateness of the different copula functions. We also compare the suggested copula models to a standard variance-covariance approach and a multivariate GARCH-BEKK model. We find significant positive correlation between the series what somehow contradicts earlier studies on the topic finding negative or only weak positive correlations between REITS and equity investments. Therefore, for Australian markets the diversification potential of investments in REITS might be less significant than for overseas markets. We also find significant tail dependence, in particular in the lower left tail that is best modeled by the Clayton copula. Conducting a back testing Value-at-Risk study for a portfolio combining investments in real estate and equity we find that the conditional copula as well as the GARCH BEKK model significantly outperform a static variance covariance approach. Our findings suggest that ignoring the complex and dynamic dependence structure in favor of a simple multivariate normal model leads to a significant underestimation of the actual risk.

Modelling dynamic dependence between crude oil prices and Asia-Pacific stock market returns

This paper investigates the dynamic dependence between crude oil prices and stock markets in ten countries across the Asia-Pacific region during the period from January 4, 2000 to March 30, 2012 by using unconditional and conditional copula models. The model is implemented using an AR (p)-GARCH (1, 1)-t model for the marginal distributions and constant and time-varying copulas for the joint distribution. The results show that the dependence between crude oil prices and Asia-Pacific stock market returns is generally weak, that it was positive before the global financial crisis, except in Hong Kong, and that it increased significantly in the aftermath of the crisis. The lower tail dependence between oil prices and Asia-Pacific stock markets exceeds that of the upper tail dependence, except in Japan and Singapore in the post-crisis period. Moreover, we show that time-varying copulas best capture the tail dependence and that taking the tail correlation into account leads to improved accuracy of VaR estimates. These findings have important implications for investors interested in Asia-Pacific markets for portfolio diversification, risk management, and international asset allocation.