scholarly journals Portfolio Risk and Dependence Modeling: Application of Factor and Copula Models

2012 ◽  
Author(s):  
Arsalan Azamighaimasi
Keyword(s):  
Factor Model ◽  
Risk Measures ◽  
Random Variable ◽  
Copula Function ◽  
Dependence Structure ◽  
Risk Modeling ◽  
Portfolio Risk ◽  
Copula Models ◽  
Dependence Modeling ◽  
T Copula

We consider portfolio credit risk modeling with a focus on two approaches, the factor model, and the copula model. While other models have received greater scrutiny, both factor and cupola models have received little attention although these are appropriate for rating-based portfolio risk analysis. We review the two models with emphasis on the joint default probability. The copula function describes the dependence structure of a multivariate random variable. In this paper, it is used as a practical to simulation of generate portfolio with different copula, we only use Gaussian and t-copula case. And we generate portfolio default distributions and study the sensitivity of commonly used risk measures with respect to the approach in modeling the dependence structure of the portfolio.  

scholarly journals Sum of Bernoulli Mixtures: Beyond Conditional Independence

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Taehan Bae ◽  
Ian Iscoe
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Random Variable ◽  
Dependence Structure ◽  
Sample Distribution ◽  
Mixing Distribution ◽  
Bernoulli Random Variables ◽  
New Class ◽  
Bernoulli Mixtures ◽  
Conditional Tail Expectation

We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we calldouble mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model.

scholarly journals Dependence Modelling in Insurance via Copulas with Skewed Generalised Hyperbolic Marginals

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Vitali Alexeev ◽  
Katja Ignatieva ◽  
Thusitha Liyanage
Keyword(s):  
Value At Risk ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Portfolio Risk ◽  
Total Risk ◽  
Copula Models ◽  
Out Of Sample ◽  
Upper Tail Dependence ◽  
Dependence Modelling ◽  
Best Fit

Abstract This paper investigates dependence among insurance claims arising from different lines of business (LoBs). Using bivariate and multivariate portfolios of losses from different LoBs, we analyse the ability of various copulas in conjunction with skewed generalised hyperbolic (GH) marginals to capture the dependence structure between individual insurance risks forming an aggregate risk of the loss portfolio. The general form skewed GH distribution is shown to provide the best fit to univariate loss data. When modelling dependency between LoBs using one-parameter and mixture copula models, we favour models that are capable of generating upper tail dependence, that is, when several LoBs have a strong tendency to exhibit extreme losses simultaneously. We compare the selected models in their ability to quantify risks of multivariate portfolios. By performing an extensive investigation of the in- and out-of-sample Value-at-Risk (VaR) forecasts by analysing VaR exceptions (i.e. observations of realised portfolio value that are greater than the estimated VaR), we demonstrate that the selected models allow to reliably quantify portfolio risk. Our results provide valuable insights with regards to the nature of dependence and fulfils one of the primary objectives of the general insurance providers aiming at assessing total risk of an aggregate portfolio of losses when LoBs are correlated.

scholarly journals A Comprehensive Statistical Analysis of the Six Major Crypto-Currencies from August 2015 through June 2020

2020 ◽  
Vol 13 (9) ◽  
pp. 192
Author(s):  
Beatriz Vaz de Melo Mendes ◽  
André Fluminense Carneiro
Keyword(s):  
Statistical Analysis ◽  
Value At Risk ◽  
Risk Measures ◽  
Value Theory ◽  
Dependence Structure ◽  
Copula Models ◽  
Underlying Distribution ◽  
First Semester ◽  
Long Run ◽  
Daily Data

After more than a decade of existence, crypto-currencies may now be considered an important class of assets presenting some unique appealing characteristics but also sharing some features with real financial assets. This paper provides a comprehensive statistical analysis of the six most important crypto-currencies from the period 2015–2020. Using daily data we (1) showed that the returns present many of the stylized facts often observed for stock assets, (2) modeled the returns underlying distribution using a semi-parametric mixture model based on the extreme value theory, (3) showed that the returns are weakly autocorrelated and confirmed the presence of long memory as well as short memory in the GARCH volatility, (4) used an econometric approach to compute risk measures, such as the value-at-risk, the expected shortfall, and drawups, (5) found that the crypto-coins’ price trajectories do not contain speculative bubbles and that they move together maintaining the long run equilibrium, and (6) using static and dynamic D-vine pair-copula models, assessed the true dependence structure among the crypto-assets, obtaining robust copula based bivariate dynamic measures of association. The analyses indicate that the strength of dependence among the crypto-currencies has increased over the recent years in the cointegrated crypto-market. The conclusions reached will help investors to manage risk while identifying opportunities for alternative diversified and profitable investments. To complete the analysis we provide a brief discussion on the effects of the COVID-19 pandemic on the crypto-market by including the first semester of 2020 data.

Estimation and Simulation of Copula Function: An Application to Daily Korean Treasury and A-Rated Corporate Spot Rates

2003 ◽  
Vol 11 (2) ◽  
pp. 103-131
Author(s):  
Myeong Jig Kim ◽  
Seong Hwan Sin
Keyword(s):  
Copula Function ◽  
Dependence Structure ◽  
Fat Tails ◽  
Multivariate Distributions ◽  
Credit Risks ◽  
Dimensional Distribution ◽  
T Copula ◽  
Reasonable Description ◽  
Daily Changes ◽  
Individual Series

A Copula function is an useful tool for constructing and simulating multivariate distributions. It relates one-dimensional marginals with multi-dimensional distribution. By doing so, one can separately model the distribution of individual series and the dependence structure and the estimation becomes a much simpler problem. As such, data simulated from a copula allows one to price complex financial products that would be impossible otherwise and to measure both market and credit risks more realistically and accurately. This paper intends to summarize the copula methodology and applies it to the problem of simulating default-free and risky spot rates. More specifically, this paper estimates the dependence structure of daily Korean Treasury and A-rated corporate spot rates (3-year to maturity) for the 1/2/01~11/11/02 period using t-marginals and bivariate t-copula. The data appear to support the empirical fact that these rates have fat-tails and t_(3.7)-copula seems to be the reasonable description of the daily changes in spot rates. This paper also demonstrates the simulation of the data from t_(3.7)-copula.

RISK MANAGEMENT UNDER A FACTOR STOCHASTIC VOLATILITY MODEL

2011 ◽  
Vol 28 (01) ◽  
pp. 65-80 ◽  
Author(s):  
MARCOS ESCOBAR ◽  
PABLO OLIVARES
Keyword(s):  
Risk Management ◽  
Stochastic Volatility ◽  
Value At Risk ◽  
Factor Model ◽  
Risk Measures ◽  
Stochastic Volatility Model ◽  
Dependence Structure ◽  
Black Scholes Model ◽  
Volatility Model ◽  
Black Scholes

In this paper, we study risk measures and portfolio problems based on a Stochastic Volatility Factor Model (SVFM). We analyze the sensitivity of Value at Risk (VaR) and Expected Shortfall (ES) to the changes in the parameters of the model. We compare the positions of a linear portfolio under assets following a SVFM, a Black–Scholes Model and a model with constant dependence structure. We consider an application to a portfolio of three selected Asian funds.

scholarly journals New Families of Bivariate Copulas via Unit Lomax Distortion

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 106
Author(s):  
Fadal Abdullah-A Aldhufairi ◽  
Ranadeera G.M. Samanthi ◽  
Jungsywan H. Sepanski
Keyword(s):  
Random Variable ◽  
Copula Function ◽  
Unit Interval ◽  
Copula Model ◽  
Copula Models ◽  
Density Distributions ◽  
New Family ◽  
Concordance Order ◽  
Bivariate Copula

This article studies a new family of bivariate copulas constructed using the unit-Lomax distortion derived from a transformation of the non-negative Lomax random variable into a variable whose support is the unit interval. Existing copulas play the role of the base copulas that are distorted into new families of copulas with additional parameters, allowing more flexibility and better fit to data. We present general forms for the new bivariate copula function and its conditional and density distributions. The properties of the new family of the unit-Lomax induced copulas, including the tail behaviors, limiting cases in parameters, Kendall’s tau, and concordance order, are investigated for cases when the base copulas are Archimedean, such as the Clayton, Gumbel, and Frank copulas. An empirical application of the proposed copula model is presented. The unit-Lomax distorted copula models outperform the base copulas.

scholarly journals Conditional Dependence between Oil Prices and Exchange Rates in BRICS Countries: An Application of the Copula-GARCH Model

2019 ◽  
Vol 12 (2) ◽  
pp. 99
Author(s):  
Yijin He ◽  
Shigeyuki Hamori
Keyword(s):  
Exchange Rates ◽  
Value At Risk ◽  
Tail Dependence ◽  
Oil Prices ◽  
Dependence Structure ◽  
Copula Models ◽  
Conditional Dependence ◽  
Brics Countries ◽  
T Copula ◽  
Student’S T

We studied the dependence structure between West Texas Intermediate (WTI) oil prices and the exchange rates of BRICS1 countries, using copula models. We used the Normal, Plackett, rotated-Gumbel, and Student’s t copulas to measure the constant dependence, and we captured the dynamic dependence using the Generalized Autoregressive Score with the Student’s t copula. We found that negative dependence and significant tail dependence exist in all pairs considered. The Russian Ruble (RUB)–WTI pair has the strongest dependence. Moreover, we treated five exchange rate–oil pairs as portfolios and evaluated the Value at Risk and Expected Shortfall from the time-varying copula models. We found that both reach low values when the oil price falls sharply.

scholarly journals Modeling risk dependence and portfolio VaR forecast through vine copula for cryptocurrencies

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0242102
Author(s):  
Khreshna Syuhada ◽  
Arief Hakim
Keyword(s):  
Value At Risk ◽  
Risk Model ◽  
Forecast Accuracy ◽  
Dependence Structure ◽  
Financial Risks ◽  
Portfolio Risk ◽  
Dependence Modeling ◽  
Vine Copula ◽  
Dependence Assumption ◽  
Marginal Risk

Risk in finance may come from (negative) asset returns whilst payment loss is a typical risk in insurance. It is often that we encounter several risks, in practice, instead of single risk. In this paper, we construct a dependence modeling for financial risks and form a portfolio risk of cryptocurrencies. The marginal risk model is assumed to follow a heteroscedastic process of GARCH(1,1) model. The dependence structure is presented through vine copula. We carry out numerical analysis of cryptocurrencies returns and compute Value-at-Risk (VaR) forecast along with its accuracy assessed through different backtesting methods. It is found that the VaR forecast of returns, by considering vine copula-based dependence among different returns, has higher forecast accuracy than that of returns under prefect dependence assumption as benchmark. In addition, through vine copula, the aggregate VaR forecast has not only lower value but also higher accuracy than the simple sum of individual VaR forecasts. This shows that vine copula-based forecasting procedure not only performs better but also provides a well-diversified portfolio.

Impact of factor models on portfolio risk measures: a structural approach

2012 ◽  
Vol 8 (2) ◽  
pp. 47-79 ◽  
Author(s):  
Marcos Escobar ◽  
Tobias Frielingsdorf ◽  
Rudi Zagst
Keyword(s):  
Risk Measures ◽  
Factor Models ◽  
Structural Approach ◽  
Portfolio Risk

scholarly journals Dependence Modeling in Energy Markets using Sibuya-type Copulas

2017 ◽  
Vol 6 (3) ◽  
pp. 43
Author(s):  
Nikolai Kolev ◽  
Jayme Pinto
Keyword(s):  
Goodness Of Fit ◽  
Basic Assumption ◽  
Energy Markets ◽  
Dependence Structure ◽  
Dependence Function ◽  
Dependence Modeling ◽  
Goodness Of Fit Tests ◽  
Oil And Natural Gas ◽  
Error Terms ◽  
Time Invariant

The dependence structure between 756 prices for futures on crude oil and natural gas traded on NYMEX is analyzed  using  a combination of novel time-series and copula tools.  We model the log-returns on each commodity individually by Generalized Autoregressive Score models and account for dependence between them by fitting various copulas to corresponding  error terms. Our basic assumption is that the dependence structure may vary over time, but the ratio between the joint distribution of error terms and the product of marginal distributions (e.g., Sibuya's dependence function) remains the same, being time-invariant.  By performing conventional goodness-of-fit tests, we select the best copula, being member of the currently  introduced class of  Sibuya-type copulas.

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