Copula-based Approach Research Articles

Multivariate Option Pricing with Gaussian Mixture Distributions and Mixed Copulas

Recently, it has been reported that the hypothesis proposed by the classical black scholes model to price multivariate options in finance were unrealistic, as such, several other methods have been introduced over the last decades including the copulas methods which uses copulas functions to model the dependence structure of underlying assets. However, the previous work did not take into account the use of mixed copulas to assess the underlying assets' dependence structure. The approach we propose consists of selecting the appropriate mixed copula’s structure which captures as much information as possible about the asset’s dependence structure and apply a copulas-based martingale strategy to price multivariate equity options using monte Carlo simulation. A mixture of normal distributions estimated with the standard EM algorithm is also considered for modeling the marginal distribution of financial asset returns. Moreover, the Monte Carlo simulation is performed to compute the values of exotic and up and out barrier options such as worst of, spread, and rainbow options, which shows that the clayton gumble and clayton gaussian have relatively large values for all the options. Our results further indicate that the mixed copula-based approach can be used efficiently to capture heterogeneous dependence structure existing in multivariate assets, price exotic options and generalize the existing results.

Copula approach to exchange-correlation hole in many-electron systems with strong correlations

Electronic correlation is a fundamental topic in many-electron systems. To characterize this correlation, one may introduce the concept of exchange-correlation hole. In this work, we first briefly revisit its definition and relation to electron and geminal densities, followed by their intimate relations to copula functions in probability theory and statistics. We then propose a copula-based approach to estimate the exchange-correlation hole from the electron density. It is anticipated that the proposed scheme will become a promising ingredient towards the future development of strongly correlated electronic structure calculations.

Two-Sample Problems for Survival Time—A Copula-Based Approach for Dependent Censoring—

Two-Sample Problems for Survival Time—A Copula-Based Approach for Dependent Censoring—

Jointly analyzing freeway primary and secondary crash severity using a copula-based approach

A copula-based model is developed in this study to jointly model the severity of freeway primary crashes and secondary crashes. The copula-based model can concurrently account for the severity levels in the crash and the correlation among primary-secondary crash pairs’ severity. The model comprehensively considers a series of explanation variables, including temporal characteristics, crash characteristics, roadway characteristics and real-traffic conditions, and is estimated using traffic crash data from 2016 through 2019 for Los Angeles County, California. The proposed copula model is then contrasted with the traditional binary probit model and the results show a remarkable advantage of the copula model, which is evidenced by better fitting performance. It is found that weather, whether towed away, unsafe speed, collision type, road condition, terrain, road weaving and truck involvement have significant impact on primary crash severity propensity and collision type, road width, road condition, traffic volume and vehicle speed have significant impact on secondary crash severity propensity. In light of the findings, a number of countermeasures are proposed to mitigate freeway crashes, including emergency services, vehicle and roadway engineering, traffic law enforcement and driver education.

A Bayesian network to analyse basketball players’ performances: a multivariate copula-based approach

Statistics in sports plays a key role in predicting winning strategies and providing objective performance indicators. Despite the growing interest in recent years in using statistical methodologies in this field, less emphasis has been given to the multivariate approach. This work aims at using the Bayesian networks to model the joint distribution of a set of indicators of players’ performances in basketball in order to discover the set of their probabilistic relationships as well as the main determinants affecting the player’s winning percentage. From a methodological point of view, the interest is to define a suitable model for non-Gaussian data, relaxing the strong assumption on normal distribution in favour of Gaussian copula. Through the estimated Bayesian network, we discovered many interesting dependence relationships, providing a scientific validation of some known results mainly based on experience. At last, some scenarios of interest have been simulated to understand the main determinants that contribute to rising in the number of won games by a player.

A Copula-Based Approach for Modelling the Dependence between Inflation and Exchange Rate in Kenya

In this study, we modeled the dependence structure between inflation and exchange rate using the copula approach. To formulate a bivariate copula, we used ARMA+GARCH to model serial dependence for each univariate series of returns. Both for in ation and exchange rate, it was found that the student t distribution was the best marginal distribution. Then, we transformed the standardized residuals from those marginal distributions (student t) into uniform over the range [0; 1]. To estimate the copula, we used a parametric approach. Gumbel copula was found to be the best to capture the dependence. We investigated the time-varying dependence using change-point detection based on copula. We found that there is a significant change in the nature of dependence over the period under consideration. The change in the nature of dependence between the two variables was in line with the prevailing macro-economics conditions during the period under review. We recommend to the future researchers to consider studying time-varying dependence between those two variables and investigate also the change in copula parameters in values with time. We also recommend including other macroeconomic variables while modeling the relationship between in ation and exchange rate.

Systemic risk measurement: A limiting threshold copula approach to CoVaR

This article proposes a novel copula-based approach to estimate CoVaR. Copula selection is based on multivariate extreme value theory rather than model fitting results. The Clayton copula as a limiting lower threshold copula is found to be able to provide a useful dependence structure for modelling the joint tail behaviour of financial returns. The out-of-sample testing of one-step quantile forecasts shows that the dynamic Clayton copula significantly outperforms the alternatives. It also shows the GJR-GARCH-Skew t model is a powerful competitor of the GPD-based models. Hence, the method provides a simple and effective way for estimating CoVaR and VaR.

A Particle Swarm Optimization Copula-Based Approach with Application to Cryptocurrency Portfolio Optimisation

Blockchain and cryptocurrency are gradually going mainstream with new cryptocurrencies introduced every single day. The speculative nature of these digital assets expose their prices to large fluctuations. Trading these crypto-assets necessitate an adequate understanding of this emerging market as well as adequate tools to model the market risk and efficient allocation of funds. This may assist crypto investors in taking advantage of the highly volatile aspects of these assets. The portfolio consider in this study consists of six cryptocurrencies: four traditional cryptocurrencies (BTC, ETH, BNB and XRP) and two stablecoins (USDT and USDC). We examine the copula particle swarm optimization (CPSO) portfolio strategy against three other portfolio strategies, namely, the global minimum variance (GMV), the most diversified portfolio (MDP) and the minimum tail dependent (MTD). CPSO appears to be a promising strategy during extreme market conditions while GMV seem favorable during normal market conditions. Most importantly, hedge and safe-havens ability of the two stablecoins is clearly exhibited with CPSO, while their diversification property is inhibited.

Optimization and Diversification of Cryptocurrency Portfolios: A Composite Copula-Based Approach

This paper focuses on the selection and optimisation of a cryptoasset portfolio, using the K-means clustering algorithm and GARCH C-Vine copula model combined with the differential evolution algorithm. This integrated approach allows the construction of a diversified portfolio of eight cryptocurrencies and determines an optimal allocation strategy making it possible to minimize the conditional value-at-risk of the portfolio and maximise the return. Our results show that stablecoins such as True-USD are negatively correlated to the other cryptoassets in the portfolio and could therefore be a safe haven for crypto-investors during market turmoil. Our findings are in line with previous studies exhibiting stablecoins as potential diversifiers.

A copula-based approach for creating an index of micronutrient intakes at household level in Pakistan

Deficiency of micronutrients is considered as the basic cause of health issues. There are a large number of micronutrients to be considered for good health, which are analyzed separately. However, such analyses involve practical as well as methodological complications and it requires construction of an index representing malnutrition of micronutrients. This study proposes copula methodology to categorize malnutrition of micronutrients at household level by combining the dependence structure of various correlated variables. Data of eleven micronutrients are extracted from HIICS- 2015–16 published by Pakistan -Bureau of Statistics. Seven out of the eleven variables are highly correlated, which are considered to construct the index. These include calcium, iron, iodine, zinc, riboflavin, thiamine and phosphorus intakes per capita at household level. Normal probability distribution is found as the best fit to the sample data of all variables. Gaussian copula function is used to derive multivariate probability distribution by combining univariate marginal probability distribution of each micronutrient. The Multivariate distribution of Gaussian copula model is used to calculate cumulative probabilities, which provide a base to categorize households’ malnutrition w.r.t. micronutrients. The results show that 60% households lie in very low or low category of micronutrient intakes, 20% of households fall into medium category while 20% fall into high or very high category of micronutrient consumption. The proposed methodology might be helpful to combine other micronutrients as well as a variety of correlated variables in many other fields having a survey data

Multivariate analysis of traffic flow using copula-based model at an isolated road intersection

Investigating the correlation relationship among traffic flow parameters (speed, time headway, volume) and accurately estimating their distribution function at urban road intersections are critical to provide theoretical support for traffic simulation in traffic management and control. Previous studies usually investigated distributions of traffic flow parameters separately, and they did not take into account the correlation between these parameters. In this study, a copula-based approach is proposed to analyze the dependence structure and model the multivariate distribution of traffic flow parameters during peak and off-peak hours in three directions at the intersections. First, the correlation between the traffic flow parameters/variables is examined by Kendall’s tau and Spearman’s rho to measure the correlation relationship. Then, fitting marginal distributions for traffic variables is conducted. The distribution function with the best fitting performance of each traffic variable is selected based on AIC and K–S tests. Moreover, copula-based models that employ Gaussian, FGM, Gumbel, Clayton, Frank and AMH copula functions are used to construct the bivariate joint distribution. The optimal copula model is selected by using the log-likelihood and AIC to evaluate fitting results. Finally, by comparing the observed data with the same size simulated data generated from the best fitting copula model, we find that the copula-based model could accurately construct the bivariate joint distribution and reproduce the dependence structure between the variables. Overall, the findings of this study provide an in-depth perspective on the dependence structure of traffic variables at urban road intersections.

Toward coupling of groundwater drawdown and pumping time in a constant discharge

Groundwater is considered an essential water resource in arid and semi-arid regions such as Iran. This study used a copula-based approach to analyze the joint frequency of groundwater level and the duration of groundwater pumping with a constant discharge. In particular, this study examines the correlation between the pumping time and groundwater drawdown variables for two cases of 26.6 and 28.8 l/s constant discharges and a pumping time of 220 min. In addition, the Weibull probability distribution and Galambos copula were used for these two tests. To estimate the groundwater drawdown at different pumping times with different probabilities, the obtained typical curves by providing the contour curves of the cumulative groundwater drawdown probability and the pumping time in both tests were obtained. For example, for 150 min of pumping, the groundwater drawdown for pumping discharge of 26.64 and 28.8 l/s with a 60% probability is about 7.4 and 8 m, respectively. The results of the joint-occurrence frequency analysis in the study area showed that for each unit of increase in pumping discharge in the pumping well, a drawdown of 0.32 m is imaginable in the observation well. In the next step, the groundwater drawdown got analyzed in both tests simultaneously. Since the pumping time is the same, the effect of increasing the pumping discharge in the study area is observable in the joint-occurrence probability curve.

Development of a risk-based optimization approach to improve the performance of urban drainage systems

ABSTRACT Considering the great deal of rainfall uncertainty in urban drainage system (UDS) design/rehabilitation, a copula-based design approach is developed within a Monte Carlo simulation (MCS) to improve system performance. Firstly, inundation zones are determined using HEC-RAS 2D and GIS tools. Then, inundation zones of flood scenarios are integrated with damage–depth functions in GIS to obtain the associated damage costs. Accordingly, a mapping is made between the flood volume (calculated by EPA-SWMM) and its related damage. This information is used in a coupled EPA-SWMM and differential evolution (DE) search algorithm to determine the best rehabilitation strategies. The approach is applied to a catchment in Tehran and its results are compared with the return-period method. Results show that the risk-based design approach could provide a 92% reduction in expected annual flood damage (EAD) and presents optimal designs with benefit-to-cost ratios up to 11, according to budget level. This approach yields more robust designs/strategies relative to the return-period method.

Surrogate-assisted seismic performance assessment incorporating vine copula captured dependence

Performance-based earthquake engineering (PBEE) is an advanced philosophy for the design, assessment, and decision-making of structures under seismic hazards. Improving the accuracy and efficiency of PBEE is of great importance. In traditional cloud analysis, a linear regression is performed in the logarithmic space of seismic intensity measure (IM) and demand. The obtained relationship is used to predict the seismic demand. Then, some advanced models for seismic demand prediction were developed to improve the accuracy. There exists dependence within PBEE, whereas multivariate normality of logarithmic values is widely assumed for modeling the dependence in previous studies. This paper proposes a hybrid and novel framework to improve the seismic performance assessment. The proposed framework can improve confidence while capturing more realistic dependence. The vector IM and surrogate models are coupled to predict the seismic demand. The vine copula can characterize complex nonlinear dependence structures, and it is adopted to model the dependence of demands and IMs. Then, seismic performance can be assessed. The proposed framework is illustrated on bridges under seismic hazards. For the investigated cases, the proposed framework can improve confidence significantly and better capture complex dependence. Additionally, the effect of dependence modeling on higher-order moments of seismic performance is investigated. Within the investigated cases, the large difference of higher-order moments of seismic performance is observed by using conventional assumption and vine copula. The generality and flexibility of vine copula-based approach highlight the necessity of implementing the proposed framework.

The impact of atmospheric blocking on the compounding effect of ozone pollution and temperature: a copula-based approach

Abstract. Ozone pollution and high temperatures have adverse health impacts that can be amplified by the combined effects of ozone and temperature. Moreover, changes in weather patterns are expected to alter ozone pollution episodes and temperature extremes. In particular, atmospheric blocking is a high-impact, large-scale phenomenon at mid-high latitudes that has been associated with temperature extremes. This study examines the impact of atmospheric blocking on the ozone and temperature dependence among measurement stations over Europe during the period 1999–2015. We use a copula-based method to model the dependence between the two variables under blocking and non-blocking conditions. This approach allows us to examine the impact of blocks on the joint probability distribution. Our results showed that blocks lead to increasing strength in the upper tail dependence of ozone and temperature extremes (> 95th percentile) in north-west and central Europe (e.g. the UK, Belgium, Netherlands, Luxembourg, Germany and the north-west of France). The analysis of the probability hazard scenarios revealed that blocks generally enhance the probability of compound ozone and temperature events by 20 % in a large number of stations over central Europe. The probability of ozone or temperature exceedances increases 30 % (on average) under the presence of atmospheric blocking. Furthermore, we found that, in a number of stations over north-western Europe, atmospheric blocking increases the probability of ozone exceedances by 30 % given high temperatures. Our results point out the strong influence of atmospheric blocking on the compounding effect of ozone and temperature events, suggesting that blocks might be considered a relevant predicting factor when assessing the risks of ozone-heat-related health effects.

A copula-based approach to accommodate intra-household interaction in workers’ daily maintenance activity stop generation modeling

A new stop frequency model was developed to predict the daily number of maintenance activity stops made by individual household heads during a typical weekday. This new model was based on the modification of a conventional multivariate ordered probit (MOP) model by maintaining the probit assumption for the marginal distributions while introducing non-normal dependence among the error terms using copula functions. Therefore, the copula-based MOP model would relieve the restriction of imposing joint normality on the error terms in the conventional MOP model. The new MOP model would not only account for the intra-household interactions in stop-making decisions, but also allow the best functional form to be determined for representing dependencies among household heads. Using the New York Metropolitan Transportation Council's 2010/2011 regional household travel survey data, the copula-based MOP model was employed to examine stop-making behavior for individual household heads residing in New York City and its adjacent counties in Mid-Hudson Valley and New Jersey. Empirical results provided useful insights into the observed effects of socio-demographics, land use density, transportation service, and work schedule together with potential unobserved common effects on the inter-relatedness of spousal stop-making decisions at the household level. The results show that the MOP model with a Clayton copula structure provides the best data fits and there is a very strong positive dependence among error terms of stop-making equations. Furthermore, the dependence among the maintenance activity propensities of household heads is asymmetric, with a stronger tendency of household heads to simultaneously have low maintenance activity levels than to simultaneously have high maintenance activity levels.

Volatility Modeling and Dependence Structure of ESG and Conventional Investments

The question of whether environmental, social, and governance investments outperform or underperform other conventional financial investments has been debated in the literature. In this study, we compare the volatility of rates of return of selected ESG indices and conventional ones and investigate dependence between them. Analysis of tail dependence is important to evaluate the diversification benefits between conventional investments and ESG investments, which is necessary in constructing optimal portfolios. It allows investors to diversify the risk of the portfolio and positively impact the environment by investing in environmentally friendly companies. Examples of institutions that are paying attention to ESG issues are banks, which are increasingly including products that support sustainability goals in their offers. This analysis could be also important for policymakers. The European Banking Authority (EBA) has admitted that ESG factors can contribute to risk. Therefore, it is important to model and quantify it. The conditional volatility models from the GARCH family and tail-dependence coefficients from the copula-based approach are applied. The analysis period covered 2007 until 2019. The period of the COVID-19 pandemic has not been analyzed due to the relatively short time series regarding data requirements from models’ perspective. Results of the research confirm the higher dependence of extreme values in the crisis period (e.g., tail-dependence values in 2009–2014 range from 0.4820/0.4933 to 0.7039/0.6083, and from 0.5002/0.5369 to 0.7296/0.6623), and low dependence of extreme values in stabilization periods (e.g., tail-dependence values in 2017–2019 range from 0.1650 until 0.6283/0.4832, and from 0.1357 until 0.6586/0.5002). Diversification benefits vary in time, and there is a need to separately analyze crisis and stabilization periods.

Stress-strength reliability with dependent variables based on copula function

<p style='text-indent:20px;'>The stress-strength model is a basic model in the field of reliability, but it still has some obvious limitations in many applications. Therefore, considering different aspects and using different methods to investigate the stress-strength model has been one of the main research directions of reliability. In this paper, we suppose the problem of evaluating reliability considering the stress and strength as dependent variables when the association is modeled by the copula function. By using Monte Carlo simulation, we estimate the reliability measure <inline-formula><tex-math id="M1">\begin{document}$ R $\end{document}</tex-math></inline-formula> for dependent margins by choosing various copulas and known marginal distributions to belong to a specific class of parametric models, here the Dagum family. Finally, the application of the copula-based approach in reliability modelling is illustrated using two medical data sets. The results of these two data sets show the effectiveness of this method in reliability modelling.</p>

Social Media Integration of Flood Data: A Vine Copula-Based Approach

Floods are the most common and among the most severe natural disasters in many countries around the world. As global warming continues to exacerbate sea level rise and extreme weather, governmental authorities and environmental agencies are facing the pressing need of timely and accurate evaluations and predictions of flood risks. Current flood forecasts are generally based on historical measurements of environmental variables at monitoring stations. In recent years, in addition to traditional data sources, large amounts of information related to floods have been made available via social media. Members of the public are constantly and promptly posting information and updates on local environmental phenomena on social media platforms. Despite the growing interest of scholars towards the usage of online data during natural disasters, the majority of studies focus exclusively on social media as a stand-alone data source, while its joint use with other type of information is still unexplored. In this paper we propose to fill this gap by integrating traditional historical information on floods with data extracted by Twitter and Google Trends. Our methodology is based on vine copulas, that allow us to capture the dependence structure among the marginals, which are modelled via appropriate time series methods, in a very flexible way. We apply our methodology to data related to three different coastal locations on the South coast of the United Kingdom (UK). The results show that our approach, based on the integration of social media data, outperforms traditional methods in terms of evaluation and prediction of flood events.

Estimating the correlation between semi-competing risk survival endpoints.

Time-to-event, bivariate, semi-competing risk data occur when a terminal event can censor a non-terminal event, but not vice versa. There are potential correlations between these endpoints as they are measured on the same individual. However, traditional methods to estimate the correlations cannot be used directly due to the censoring of time-to-event endpoints. We develop methods using a copula-based approach to study the dependence structures between the two survival endpoints. We use a variety of copulas to estimate the correlation between endpoints and to acknowledge different dependence structures. The estimated association parameter in the copula function is transformed into Spearman's rank correlation coefficient. We conduct a simulation study to evaluate the estimation from the proposed models along with the effects of misspecification of the copula functions and survival distributions. The proposed methods are applied to two real-life datasets.