How correlation risk in basket credit derivatives might be priced and managed?

2020 ◽  
Author(s):  
Dong-Mei Zhu ◽  
Jia-wen Gu ◽  
Feng-Hui Yu ◽  
Wai-Ki Ching ◽  
Tak-Kuen Siu
Keyword(s):  
Credit Derivatives ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Default Correlation ◽  
Hedging Strategy ◽  
Quantitative Models ◽  
Dependent Risks ◽  
Correlation Risk ◽  
Management Of Risk

Abstract In this paper, we construct quantitative models in which the dependence structure of the firms’ default times is incorporated. Such models serve as the underlying frameworks in our proposed approach to price and hedge basket credit derivatives. Through the Gaussian copula-based method, we model the default correlation risk and develop valuation formulas for credit derivatives. Using single-name derivatives in a hedging strategy for basket credit derivatives, the utility of the delta and delta-gamma hedging techniques are examined. This enables the management of risk attributed to the changes in correlation without the need for a large number of hedging instruments. Our research contributions provide insights on how dependent risks in basket credit derivatives could be dealt with effectively.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK

2013 ◽  
Vol 16 (02) ◽  
pp. 1350007 ◽  
Author(s):  
DAMIANO BRIGO ◽  
AGOSTINO CAPPONI ◽  
ANDREA PALLAVICINI ◽  
VASILEIOS PAPATHEODOROU
Keyword(s):  
Interest Rate ◽  
Credit Derivatives ◽  
Credit Default Swaps ◽  
Credit Spread ◽  
Counterparty Risk ◽  
Default Correlation ◽  
Dynamical Models ◽  
Credit Default ◽  
The Impact

This article is concerned with the arbitrage-free valuation of bilateral counterparty risk through stochastic dynamical models when collateral is included, with possible rehypothecation. The payout of claims is modified to account for collateral margining in agreement with International Swap and Derivatives Association (ISDA) documentation. The analysis is specialized to interest-rate and credit derivatives. In particular, credit default swaps are considered to show that a perfect collateralization cannot be achieved under default correlation. Interest rate and credit spread volatilities are fully accounted for, as is the impact of re-hypothecation, collateral margining frequency, and dependencies.

scholarly journals Bivariate Hydrologic Risk Assessment of Flood Episodes using the Notation of Failure Probability

2020 ◽  
Vol 6 (10) ◽  
pp. 2002-2023
Author(s):  
Shahid Latif ◽  
Firuza Mustafa
Keyword(s):  
Failure Probability ◽  
Goodness Of Fit ◽  
Peak Flow ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Distribution Analysis ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Flood Peak ◽  
Flood Volume

Floods are becoming the most severe and challenging hydrologic issue at the Kelantan River basin in Malaysia. Flood episodes are usually thoroughly characterized by flood peak discharge flow, volume and duration series. This study incorporated the copula-based methodology in deriving the joint distribution analysis of the annual flood characteristics and the failure probability for assessing the bivariate hydrologic risk. Both the Archimedean and Gaussian copula family were introduced and tested as possible candidate functions. The copula dependence parameters are estimated using the method-of-moment estimation procedure. The Gaussian copula was recognized as the best-fitted distribution for capturing the dependence structure of the flood peak-volume and peak-duration pairs based on goodness-of-fit test statistics and was further employed to derive the joint return periods. The bivariate hydrologic risks of flood peak flow and volume pair, and flood peak flow and duration pair in different return periods (i.e., 5, 10, 20, 50 and 100 years) were estimated and revealed that the risk statistics incrementally increase in the service lifetime and, at the same instant, incrementally decrease in return periods. In addition, we found that ignoring the mutual dependency can underestimate the failure probabilities where the univariate events produced a lower failure probability than the bivariate events. Similarly, the variations in bivariate hydrologic risk with the changes of flood peak in the different synthetic flood volume and duration series (i.e., 5, 10, 20, 50 and 100 years return periods) under different service lifetimes are demonstrated. Investigation revealed that the value of bivariate hydrologic risk statistics incrementally increases over the project lifetime (i.e., 30, 50, and 100 years) service time, and at the same time, it incrementally decreases in the return period of flood volume and duration. Overall, this study could provide a basis for making an appropriate flood defence plan and long-lasting infrastructure designs. Doi: 10.28991/cej-2020-03091599 Full Text: PDF

HEDGING OF SYNTHETIC CDO TRANCHES WITH SPREAD AND DEFAULT RISK BASED ON A COMBINED FORECASTING APPROACH

2019 ◽  
Vol 22 (02) ◽  
pp. 1850057
Author(s):  
WEN-QIONG LIU ◽  
WEN-LI HUANG
Keyword(s):  
Default Risk ◽  
Credit Derivatives ◽  
Point Of View ◽  
Gaussian Copula ◽  
Collateralized Debt Obligations ◽  
Market Theory ◽  
Hedging Strategies ◽  
Hedge Ratios ◽  
Local Intensity ◽  
Combined Forecasting

Hedging of credit derivatives, especially the Collateralized Debt Obligations (CDOs), is the prerequisite of risk management in financial market. Since both spread risk and default risk exist, the models in existing literature resort to the incomplete-market theory to derive the hedging strategies. From another point of view, the construction of hedging strategies of CDO might be regarded as the process of forecasting the changes in value of CDO by the changes in value of hedging instruments. Based on this idea, this paper proposes an alternative hedging approach via the combined forecasting and regression techniques, where the two individual forecasting models are Gaussian copula model and local intensity model, used to hedge against spread risk and default risk, respectively. Finally, the dynamic hedge ratios of CDO tranches with CDS index are derived. A numerical analysis is carried out and the hedge ratios obtained by the new models are compared with those from actual market spreads. It is shown that the model derived in this paper not only provides hedging strategies which agree with the market hedge ratios but that can be effectively implemented as well.

scholarly journals Drought Risk Analysis in the Eastern Cape Province of South Africa: The Copula Lens

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1938 ◽  
Author(s):  
Christina M. Botai ◽  
Joel O. Botai ◽  
Abiodun M. Adeola ◽  
Jaco P. de Wit ◽  
Katlego P. Ncongwane ◽  
...  
Keyword(s):  
South Africa ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Drought Risk ◽  
Eastern Cape Province ◽  
Return Periods ◽  
Eastern Cape ◽  
Copula Functions ◽  
Drought Duration ◽  
Drought Duration And Severity

This research study was carried out to investigate the characteristics of drought based on the joint distribution of two dependent variables, the duration and severity, in the Eastern Cape Province, South Africa. The drought variables were computed from the Standardized Precipitation Index for 6- and 12-month accumulation period (hereafter SPI-6 and SPI-12) time series calculated from the monthly rainfall data spanning the last five decades. In this context, the characteristics of climatological drought duration and severity were based on multivariate copula analysis. Five copula functions (from the Archimedean and Elliptical families) were selected and fitted to the drought duration and severity series in order to assess the dependency measure of the two variables. In addition, Joe and Gaussian copula functions were considered and fitted to the drought duration and severity to assess the joint return periods for the dual and cooperative cases. The results indicate that the dependency measure of drought duration and severity are best described by Tawn copula families. The dependence structure results suggest that the study area exhibited low probability of drought duration and high probability of drought severity. Furthermore, the multivariate return period for the dual case is found to be always longer across all the selected univariate return periods. Based on multivariate analysis, the study area (particularly Buffalo City, OR Tambo and Alfred Zoo regions) is determined to have higher/lower risks in terms of the conjunctive/cooperative multivariate drought risk (copula) probability index. The results of the present study could contribute towards policy and decision making through e.g., formulation of the forward-looking contingent plans for sustainable management of water resources and the consequent applications in the preparedness for and adaptation to the drought risks in the water-linked sectors of the economy.

scholarly journals Asymptotic Tail Probabilities for Large Claims Reinsurance of a Portfolio of Dependent Risks

2008 ◽  
Vol 38 (1) ◽  
pp. 147-159 ◽  
Author(s):  
Alexandru V. Asimit ◽  
Bruce L. Jones
Keyword(s):  
Dependence Structure ◽  
Tail Probabilities ◽  
Insurance Contracts ◽  
Dependent Risks ◽  
Asymptotic Tail

We consider a dependent portfolio of insurance contracts. Asymptotic tail probabilities of the ECOMOR and LCR reinsurance amounts are obtained under certain assumptions about the dependence structure.

scholarly journals ESTIMASI NILAI CONDITIONAL VALUE AT RISK MENGGUNAKAN FUNGSI GAUSSIAN COPULA

2015 ◽  
Vol 4 (4) ◽  
pp. 188
Author(s):  
HERLINA HIDAYATI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA
Keyword(s):  
At Risk ◽  
Confidence Level ◽  
Value At Risk ◽  
Risk Measure ◽  
Copula Function ◽  
Gaussian Copula ◽  
Nonlinear Dependence ◽  
Conditional Value At Risk ◽  
Dependence Structure ◽  
Measurement Tools

Copula is already widely used in financial assets, especially in risk management. It is due to the ability of copula, to capture the nonlinear dependence structure on multivariate assets. In addition, using copula function doesn’t require the assumption of normal distribution. There fore it is suitable to be applied to financial data. To manage a risk the necessary measurement tools can help mitigate the risks. One measure that can be used to measure risk is Value at Risk (VaR). Although VaR is very popular, it has several weaknesses. To overcome the weakness in VaR, an alternative risk measure called CVaR can be used. The porpose of this study is to estimate CVaR using Gaussian copula. The data we used are the closing price of Facebook and Twitter stocks. The results from the calculation using 90%  confidence level showed that the risk that may be experienced is at 4,7%, for 95% confidence level it is at 6,1%, and for 99% confidence level it is at 10,6%.

The dependence structure in credit risk between money and derivatives markets

2014 ◽  
Vol 40 (8) ◽  
pp. 758-769
Author(s):  
Weiou Wu ◽  
David G. McMillan
Keyword(s):  
Credit Risk ◽  
Sovereign Debt ◽  
Debt Crisis ◽  
Money Market ◽  
Distribution Functions ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Content Type ◽  
Dimensional Distribution ◽  
Derivatives Markets

Purpose – The purpose of this paper is to examine the dynamic dependence structure in credit risk between the money market and the derivatives market during 2004-2009. The authors use the TED spread to measure credit risk in the money market and CDS index spread for the derivatives market. Design/methodology/approach – The dependence structure is measured by a time-varying Gaussian copula. A copula is a function that joins one-dimensional distribution functions together to form multivariate distribution functions. The copula contains all the information on the dependence structure of the random variables while also removing the linear correlation restriction. Therefore, provides a straightforward way of modelling non-linear and non-normal joint distributions. Findings – The results show that the correlation between these two markets while fluctuating with a general upward trend prior to 2007 exhibited a noticeably higher correlation after 2007. This points to the evidence of credit contagion during the crisis. Three different phases are identified for the crisis period which sheds light on the nature of contagion mechanisms in financial markets. The correlation of the two spreads fell in early 2009, although remained higher than the pre-crisis level. This is partly due to policy intervention that lowered the TED spread while the CDS spread remained higher due to the Eurozone sovereign debt crisis. Originality/value – The paper examines the relationship between the TED and CDS spreads which measure credit risk in an economy. This paper contributes to the literature on dynamic co-movement, contagion effects and risk linkages.

Sharp Bounds for Sums of Dependent Risks

2013 ◽  
Vol 50 (01) ◽  
pp. 42-53 ◽  
Author(s):  
Giovanni Puccetti ◽  
Ludger Rüschendorf
Keyword(s):  
Random Variables ◽  
Dependence Structure ◽  
Homogeneous Case ◽  
Marginal Distributions ◽  
Sharp Bounds ◽  
Duality Result ◽  
Dependent Risks ◽  
Monotone Densities ◽  
Monotone Density ◽  
Dual Bounds

Sharp tail bounds for the sum of d random variables with given marginal distributions and arbitrary dependence structure have been known since Makarov (1981) and Rüschendorf (1982) for d=2 and, in some examples, for d≥3. Based on a duality result, dual bounds have been introduced in Embrechts and Puccetti (2006b). In the homogeneous case, F 1=···=F n , with monotone density, sharp tail bounds were recently found in Wang and Wang (2011). In this paper we establish the sharpness of the dual bounds in the homogeneous case under general conditions which include, in particular, the case of monotone densities and concave densities. We derive the corresponding optimal couplings and also give an effective method to calculate the sharp bounds.

scholarly journals Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas

2018 ◽  
Vol 6 (1) ◽  
pp. 19-46 ◽  
Author(s):  
Xisong Jin ◽  
Thorsten Lehnert
Keyword(s):  
Risk Management ◽  
Value At Risk ◽  
Degrees Of Freedom ◽  
Portfolio Allocation ◽  
Optimal Portfolio ◽  
Gaussian Copula ◽  
High Dimensional ◽  
Dependence Structure ◽  
Portfolio Risk ◽  
Portfolio Risk Management

Abstract Previous research has focused on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, existing dynamic models are not easily applied to high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) for passive portfolios and dynamic optimal portfolios using Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (1) Modeling the marginal distribution is important for dynamic high-dimensional multivariate models. (2) Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3) The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (4) Grouped t-copulas and t-copulas with dynamic degrees of freedom further match the fat tail. (5) Correctly modeling the dependence structure makes an improvement in portfolio optimization with respect to tail risk. (6) Models driven by multivariate t innovations with exogenously given degrees of freedom provide a flexible and applicable alternative for optimal portfolio risk management.

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