Regime-switching Copula Research Articles

Financial and Oil Market’s Co-Movements by a Regime-Switching Copula

Over the years, oil prices and financial stock markets have always had a complex relationship. This paper analyzes the interactions and co-movements between the oil market (WTI crude oil) and two major stock markets in Europe and the US (the Euro Stoxx 50 and the SP500) for the period from 1990 to 2023. For that, I use both the time-varying and the Markov copula models. The latter one represents an extension of the former one, where the constant term of the dynamic dependence parameter is driven by a hidden two-state first-order Markov chain. It is also called the dynamic regime-switching (RS) copula model. To estimate the model, I use the inference function for margins (IFM) method together with Kim’s filter for the Markov switching process. The marginals of the returns are modeled by the GARCH and GAS models. Empirical results show that the RS copula model seems adequate to measure and evaluate the time-varying and non-linear dependence structure. Two persistent regimes of high and low dependency have been detected. There was a jump in the co-movements of both pairs during high regimes associated with instability and crises. In addition, the extreme dependence between crude oil and US/European stock markets is time-varying but also asymmetric, as indicated by the SJC copula. The correlation in the lower tail is higher than that in the upper. Hence, oil and stock returns are more closely joined and tend to co-move more closely together in bullish periods than in bearish periods. Finally, the dependence between WTI crude oil and the SP500 stock index seems to be more affected by exogenous shocks and instability than the oil and European stock markets.

Dependence Structure of the US Dollar Index and Crude Oil Prices: A Regime-Switching Copula Approach

Dependence Structure of the US Dollar Index and Crude Oil Prices: A Regime-Switching Copula Approach

Relationship between the S&P 500 index and its constituents: A regime-switching copula approach and a model-free asymmetry test

Relationship between the S&P 500 index and its constituents: A regime-switching copula approach and a model-free asymmetry test

A regime-switching real-time copula GARCH model for optimal futures hedging

A regime-switching real-time copula GARCH (RSRTCG) model is suggested for optimal futures hedging. The specification of RSRTCG is to model the margins of asset returns with state-dependent real-time GARCH and the dependence structure of asset returns with regime switching copula functions. RSRTCG is faster in adjusting to the new level of volatility under different market regimes which is a regime-switching multivariate generalization of the state-independent univariate real-time GARCH. RSRTCG is applied to cross hedge the price risk of S&P 500 sector indices with crude oil futures. The empirical results show that RSRTCG possesses superior hedging performance compared to its nested non-real-time or state-independent copula GARCH models based on the criterion of percentage variance reduction, utility gain, model confidence set, model combination strategy, risk-adjusted return and reward-to-semivariance ratio.

MEASURING FINANCIAL MARKET RISK CONTAGION BETWEEN CHINESE AND OTHER ONE BELT ONE ROAD COUNTRIES’ STOCK MARKETS

In this paper, we employ the dynamic Markov regime-switching copula model to measure the financial risk contagion among the One Belt One Road (OBOR) countries. To investigate the impact of the OBOR initiative, we divide the sample period into two subsamples and calculate the daily low/high tail dependence by adopting international stock market index data from January 2004 to March 2020. The results provide evidence of financial risk contagion effects, an asymmetric risk spillover and increased tail dependence between the Chinese stock market and those of other OBOR countries.

Flight-to-quality in the stock–bond return relation: a regime-switching copula approach

This paper examines the existence, intensity and international dependence of flight-to-quality from stocks to government bonds. To this end, we develop a two-state regime-switching bivariate copula model and apply it to the domestic and cross-country stock–bond return pairs of six developed countries (France, Germany, Japan, Switzerland, the UK and the US) over the period 1999–2019. We find that US and UK government bonds have played a primary role of safe-haven assets during stock market downturns. The remaining government bond markets show the evidence of flight-to-quality, but its intensity is relatively weak. Further, we find that although flight-to-quality tends to occur simultaneously in multiple countries, the frequency of the joint occurrence varies across government bond markets.

Contagion risk between the shipping freight and stock markets: Evidence from the recent US-China trade war

This paper employs the tri-variate Markov regime-switching (MRS) copula model to investigate the dynamic dependence between the shipping freight and stock markets. Stronger contemporaneous and bidirectional lead-lag relationships between the two markets are detected in the contagion regime, which, however, are weaker in the normal regime. Compared with the Chinese stock market, the US stock market can affect and be affected by the shipping freight market in a more sensitive manner. Additionally, contagion risk between the two markets increases in most cases due to a decrease in the volume of the US-China trade. The results have important implications for market prediction and risk management.

A risk analysis of step-down equity-linked securities based on regime-switching copula

The globalization of financial markets has broadened investment opportunities. International investors’ investment portfolios consist of financial instruments from various countries; consequently, the risks associated with economic dependence among countries should be carefully considered. Step-down equity-linked securities (ELS) are a structured financial product that have recently become popular among Korean investors. Payoffs are based on two or three stock indices from different regions; therefore, dependence between the indices should be reflected in the risk analysis. In this study, we consider a regime-switching copula model to describe the joint behavior of two stock indices- the Eurostoxx50 and the Hang Seng China Enterprises Index (HSCEI). These indices are commonly used as underlying assets of step-down ELS. Using historical data, we analyze the risk associated with step-down ELS through the probabilities of early redemption. A regime-switching copula model can accommodate complicated dependence. Thus, it should be considered in the risk analysis of step-down ELS.

MODELLING MORTALITY DEPENDENCE WITH REGIME-SWITCHING COPULAS

AbstractWe propose a two-regime Markov switching copula to depict the evolution of mortality dependence. One regime represents periods of high dependence and the other regime represents periods of low dependence. Each regime features a regular vine (R-vine) copula that, built on bivariate copulas, provides great flexibility for modelling complex high-dimensional dependence. Our estimated model indicates that the years of recovery from extreme mortality deterioration and the years of health care reform more likely fall into the low regime, while the years in which extreme mortality deteriorating events break out and the peaceful years without major mortality-impacting events more likely fall into the high regime. We use a case study to illustrate how the regime-switching copula can be applied to assess the effectiveness of longevity risk hedge with different beliefs about future mortality dependence evolution incorporated.

Goodness-of-Fit for Regime-Switching Copula Models with Application to Option Pricing

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of- fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

Estimation and Goodness-of-Fit for Regime-Switching Copula Models with Application

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of-fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

Contagion and bond pricing: The case of the ASEAN region

In this paper, we obtain explicit numerical formulas to price the defaultable bonds prices of firms. The possible default event of the firms happen in random time and not necessary in uniform time spread. For this purpose, we develop a Markov regime-switching Copula model that allows us to well-capture the economic behavior in some ASEAN region countries. The first regime represents the evidence that is used to support the standard economy. The second regime represents the crisis state. Based on various specifications, we obtain an explicit formula to evaluate the conditional Laplace transform of a regime switching Cox Ingersoll Ross model using the semi-affine property of this model. Our numerical results show strong evidence for increasing volatility parameter in crisis state, suggesting more possibility of contagion. Furthermore, statistically significant differences in terms of volatility of default across countries are reported. Indonesia and Malaysia exhibit particularly higher volatility than other markets, especially in the crisis state.

Are Islamic bonds a good safe haven for stocks? Implications for portfolio management in a time-varying regime-switching copula framework

ABSTRACTWe examine the portfolio implications of adding the Islamic bond index (Sukuk) to a benchmark portfolio of Islamic stocks. The daily data of the Islamic bond index; the Islamic stock markets of the world, Canada, Japan, USA, UK and Islamic financial stocks are used for the period of 1 October 2005 through 30 April 2015. We examine the presence of structural breaks via the Iterated Cumulative Sum of Square (ICSS) algorithm, which clearly indicate that Islamic stock-bond returns have several structural breaks over the sample period; hence, the dependence among the markets may have a regime-switching pattern. We rely on the flexible properties of the ARMA-FIGARCH models with the skew-t distribution to model the marginal distributions of the series. Next, a set of static, time-varying and regime-switching time-varying copula models are applied to encircle the dependence dynamics. Finally, using different portfolio strategies, we access the portfolio implications of a multi-asset portfolio. Overall, the results provide evidence that the Islamic bond index can be included as a potential hedge/safe haven in benchmark stock portfolios.

Measuring financial contagion between major european stock markets via the regime-switching vine copula model

Using regime-switching copula models, this study investigates co-movements of financial markets, including four major stock markets of European countries (UK, French, Germany, and Italy) in stable, stressful, and extremely stressful market conditions during 2004–2017. We introduce vine copulas to describe high-dimensional dependence structure between markets in modelling. In addition, we integrate copula methods with advanced regime-switching detection to identify different volatility regimes. Because of the characteristics of stock returns, we also release the assumption of joint normality to capture markets' tail dependence. The results show increasing tail dependence and asymmetry during stressful and extremely stressful market conditions, validating the financial contagion phenomenon, the spread of market turmoil. Further, our findings show continuing risk spillover after the 2008 financial crisis. The lasting effects make markets vulnerable for a long time after the crisis, which may be a cause of the decreasing time intervals between financial crises in recent years. Moreover, before the crisis the tail dependence strengthened first in the low volatility regime, followed by joint volatility strengthening between markets. Therefore, observing changes in tail dependence may provide early warnings of the next financial crisis.

A regime-switching copula approach to modeling day-ahead prices in coupled electricity markets

The recent price coupling of many European electricity markets has triggered a fundamental change in the interaction of day-ahead prices, challenging additionally the modeling of the joint behavior of prices in interconnected markets. In this paper we propose a regime-switching AR–GARCH copula to model pairs of day-ahead electricity prices in coupled European markets. While capturing key stylized facts empirically substantiated in the literature, this model easily allows us to 1) deviate from the assumption of normal margins and 2) include a more detailed description of the dependence between prices. We base our empirical study on four pairs of prices, namely Germany–France, Germany–Netherlands, Netherlands–Belgium and Germany–Western Denmark. We find that the marginal dynamics are better described by the flexible skew t distribution than the benchmark normal distribution. Also, we find significant evidence of tail dependence in all pairs of interconnected areas we consider. As a first application of the proposed model, we consider the pricing of financial transmission rights, and highlight how the choice of marginal distributions and copula impacts prices. As a second application we consider the forecasting of tail quantiles, and evaluate the out-of-sample performance of competing models.

The contagion effect in European sovereign debt markets: A regime-switching vine copula approach

Multidimensional dependence in financial markets has motivated the conception of copulas as a tool to analyze nonlinear connections. However, the dynamics generating the dependence structure is still considered unchanged, whether during turmoil or stable periods, and the curse of dimensionality prevents researchers from detecting the regime shifting that may connect financial markets. In this paper, we develop a tractable Markov regime-switching C-vine and D-vine under the symmetrized Joe-Clayton copula, capable of detecting lower and upper tail dependencies separately. Application is conducted on twelve government bonds, the U.S. and eleven European bonds belonging to the Eurozone. Results show that the regime-switching copula models explain the dynamics of data dependence better than the single-regime copula, which indicates the presence of a contagion effect. Furthermore, for Eurozone bond markets, the contagion remains in its high state since the global financial crisis of 2008 and European sovereign debt crisis of 2009, with a transmission path from core to stressed countries.

Modeling the multivariate dynamic dependence structure of commodity futures portfolios

This paper examines the time-varying dependence structure of commodity futures portfolios based on multivariate dynamic copula models. The importance of accounting for time-variation is emphasized in the context of the Basel traffic light system. We enhance the flexibility of this structure by modeling regimes with multivariate mixture copulas and by applying the dynamic conditional correlation model (DCC) to multivariate elliptical copulas. The most suitable dynamic dependence model in terms of in-sample and out-of sample valuation is the dynamic Student-t-Clayton mixture copula, followed by the dynamic Student-t copula, and the dynamic Gaussian-Clayton mixture. In comparison to the multivariate normal model, the dynamic Clayton copula also scales down significantly the number of VaR(99%) violations during the 2007/08 financial crisis period. The predictive performance of our multivariate dynamic copula models confirms its superiority over bivariate regime-switching copula models for various states of the economy.

A Regime-Switching Copula Approach to Modeling Day-Ahead Prices in Coupled Electricity Markets

The recent price coupling of many European electricity markets has triggered a fundamental change in the interaction of day-ahead prices, challenging additionally the modeling of the joint behavior of prices in interconnected markets. In this paper we propose a regime-switching AR-GARCH copula to model pairs of day-ahead electricity prices in coupled European markets. While capturing key stylized facts empirically substantiated in the literature, this model easily allows us to 1) deviate from the assumption of normal margins and 2) include a more detailed description of the dependence between prices. We base our empirical study on four pairs of prices, namely Germany-France, Germany-Netherlands, Netherlands-Belgium and Germany-Western Denmark. We find that the marginal dynamics are better described by the flexible skew t distribution than the benchmark normal distribution. Also, we find significant evidence of tail dependence in all pairs of interconnected areas we consider. As applications of the proposed empirical model, we consider the pricing of financial transmission rights and the forecasting of tail quantiles. In both applications, we highlight the effects of the distributional assumptions for the margins and the tail dependence.

Strategic Asset Allocation for China's Foreign Reserves: A Copula Approach

AbstractIn this paper, we study strategic asset allocation for China's foreign reserves using a risk‐based approach. Four aspects of the risk management are investigated: an investment universe, dependence structure, allocation strategies under risk minimization and trade‐off between risks and returns. A regime‐switching copula model is developed to investigate the dynamic dependence between assets. One regime emphasizes a short‐term safe asset and the other regime emphasizes a long‐term safe asset. The optimal allocation is derived following two strategies: risk minimization and trade‐off between risks and returns in utility maximization with disappointment avoidance. If the central bank focuses solely on risk minimization, the asymmetries in the asset return dependence encourage the flight to safety. However, if higher risks are allowed in exchange for higher returns, even the exchange is very conservative, and the asymmetries would discourage the flight to safety. Therefore, we suggest that China should mitigate its flight to safety after 2008 and increase holdings of short‐term bank deposits, long‐term treasury bonds and euro bonds.

The optimal portfolio in respect to Expected Shortfall: a comparative study

Value at Risk plays a crucial role in the risk management. However, this risk measure has some drawbacks. The alternative risk measure is Expected Shortfall, which is rarely used, but exhibits desirable properties. In the paper, the estimation of both risk measures has been conducted, for pairs of index returns (DJIA, DAX, ATX), based on Markowitz model, the regime switching copula model and the multivariate GARCH model. The results suggest that a misspecification can cause many errors. Incorrect models cause bias of mean, especially models which do not as- sume dynamic structure of the market Both an underestimation and an overestimation of a risk has been observed. In the paper, it is shown that the measure of change in Expected Shortfall as a function of the expected return is strongly underestimated under the normal distribution assumption.