INFORMATIONALLY DYNAMIZED GAUSSIAN COPULA

2013 ◽  
Vol 16 (02) ◽  
pp. 1350008 ◽  
Author(s):  
S. CRÉPEY ◽  
M. JEANBLANC ◽  
D. WU
Keyword(s):  
Credit Risk ◽  
State Space ◽  
Cox Model ◽  
Credit Derivatives ◽  
Point Of View ◽  
Gaussian Copula ◽  
Copula Model ◽  
Counterparty Risk ◽  
Gaussian Distributions ◽  
Augmented State

In order to dynamize the static Gaussian copula model of portfolio credit risk, we introduce a model filtration made of a reference Brownian filtration progressively enlarged by the default times. This yields a multidimensional density model of default times, where, as opposed to the classical situation of the Cox model, the reference filtration is not immersed into the enlarged filtration. In mathematical terms this lack of immersion means that martingales in the reference filtration are not martingales in the enlarged filtration. From the point of view of financial interpretation this means default contagion, a good feature in the perspective of modeling counterparty wrong-way risk on credit derivatives. Computational tractability is ensured by invariance of multivariate Gaussian distributions through conditioning by some components, the ones corresponding to past defaults. Moreover the model is Markov in an augmented state-space including past default times. After a discussion of different notions of deltas, the model is applied to the valuation of counterparty risk on credit derivatives.

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.

Die Stabilität von Finanzmärkten:Wie kann die Wirtschaftspolitik Vertrauen schaffen?

2006 ◽  
Vol 55 (1) ◽  
Author(s):  
Theresia Theurl ◽  
Jan Pieter Krahnen ◽  
Thomas P. Gehrig
Keyword(s):  
Credit Risk ◽  
Financial Markets ◽  
Financial Market ◽  
Financial Institutions ◽  
Banking Sector ◽  
Public Awareness ◽  
Credit Derivatives ◽  
Point Of View ◽  
Regulatory Oversight ◽  
The Creation

AbstractFrom Theresia Theurl’s point of view financial markets exhibit certain features that turn them inherently unstable. Therefore, economic policy measures were necessary and advisable, but they should not take the shape of isolated and selected interventions. Rather, these measures of financial market supervision and regulation had to be integrated into a comprehensive concept of micro- and macroeconomic policy in order to allow the creation of stabilizing trust.In his contribution, Jan Pieter Krahnen maintains, that the systemic risk of banks and financial institutions has changed and risen in recent years. According to his view, this is due to a more widespread use of credit derivatives. Although they may cause a more efficient distribution of credit risk in the banking sector, at the same time they could mean a higher vulnerability of the banking sector to system-wide contagion effects of credit risk. As such, financial market supervision as well as the Basel II rules on Capital Standards should take into account not only the credit risk exposure of individual financial institutions, but also correlation measures of their share prices.For Thomas Gehrig, empirical anomalies demonstrate the relevance of awareness and trust in financial markets. This note would argue in favor of social policies that enhance public awareness in financial markets as a basis for trust. And so naturally, these policies need to be complemented by a strong financial order that aims at minimizing behavioral risks. He says, trust requires a regulatory framework that reduces manipulation by private as well as public interests. A competitive order complemented by strong regulatory oversight may go a long way towards generating liquid financial markets and the creation of trust. Trust by individuals, however, would be most strongly encouraged when individuals are entrusted in managing their own financial market activities including their own pension arrangements.

scholarly journals Ensemble Kalman Filtering with a Divided State-Space Strategy for Coupled Data Assimilation Problems*

2014 ◽  
Vol 142 (12) ◽  
pp. 4542-4558 ◽  
Author(s):  
Xiaodong Luo ◽  
Ibrahim Hoteit
Keyword(s):  
Data Assimilation ◽  
State Space ◽  
Point Of View ◽  
Coupled Systems ◽  
Current Status ◽  
Estimation Strategy ◽  
Coupled Subsystems ◽  
Coupled Data Assimilation ◽  
Augmented State ◽  
Lorenz 96

Abstract This study considers the data assimilation problem in coupled systems, which consists of two components (subsystems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in such systems is to concatenate the states of the subsystems into one augmented state vector, so that a standard ensemble Kalman filter (EnKF) can be directly applied. This work presents a divided state-space estimation strategy, in which data assimilation is carried out with respect to each individual subsystem, involving quantities from the subsystem itself and correlated quantities from other coupled subsystems. On top of the divided state-space estimation strategy, the authors also consider the possibility of running the subsystems separately. Combining these two ideas, a few variants of the EnKF are derived. The introduction of these variants is mainly inspired by the current status and challenges in coupled data assimilation problems and thus might be of interest from a practical point of view. Numerical experiments with a multiscale Lorenz 96 model are conducted to evaluate the performance of these variants against that of the conventional EnKF. In addition, specific for coupled data assimilation problems, two prototypes of extensions of the presented methods are also developed in order to achieve a trade-off between efficiency and accuracy.

PRICING AND HEDGING OF PORTFOLIO CREDIT DERIVATIVES WITH INTERACTING DEFAULT INTENSITIES

2008 ◽  
Vol 11 (06) ◽  
pp. 611-634 ◽  
Author(s):  
RÜDIGER FREY ◽  
JOCHEN BACKHAUS
Keyword(s):  
Markov Process ◽  
Credit Risk ◽  
Credit Derivatives ◽  
Reduced Form ◽  
Counterparty Risk ◽  
Market Data ◽  
Portfolio Credit Risk ◽  
Default State ◽  
Default Contagion ◽  
Portfolio Credit Derivatives

We consider reduced-form models for portfolio credit risk with interacting default intensities. In this class of models default intensities are modeled as functions of time and of the default state of the entire portfolio, so that phenomena such as default contagion or counterparty risk can be modeled explicitly. In the present paper this class of models is analyzed by Markov process techniques. We study in detail the pricing and the hedging of portfolio-related credit derivatives such as basket default swaps and collaterized debt obligations (CDOs) and discuss the calibration to market data.

scholarly journals Metamodel of a Large Credit Risk Portfolio in the Gaussian Copula Model

2020 ◽  
Vol 11 (4) ◽  
pp. 1098-1136
Author(s):  
Florian Bourgey ◽  
Emmanuel Gobet ◽  
Clément Rey
Keyword(s):  
Credit Risk ◽  
Gaussian Copula ◽  
Copula Model

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.

ON THE EXTREMAL DEPENDENCE COEFFICIENTS OF GAUSSIAN DISTRIBUTIONS

Vestnik NSUEM ◽  
2021 ◽  
pp. 161-167
Author(s):  
S. E. Khrushchev
Keyword(s):  
Close Correlation ◽  
Gaussian Copula ◽  
Marginal Distributions ◽  
Gaussian Distributions ◽  
Extremal Dependence ◽  
Zero Values ◽  
Coronavirus Infection ◽  
The Russian Federation ◽  
The One ◽  
The Relationship

The paper considers a way to represent the relationship between indicators in the form of copulas. Copulas are popular mathematical tools. This is due to the fact that, on the one hand, the marginal distributions of indicators are divided in the copulas, and on the other hand, the structure of the relationship between these marginal distributions is divided, which makes it  possible to very effectively study the connections that arise in real  populations. Special attention in the work is paid to extremal dependence coefficients - important numerical characteristics of the connection in conditions of extreme small or extremely large values of indicators. It is shown that even under conditions of close correlation between the indices for a two-dimensional Gaussian distribution, the lower and upper coefficients of the extreme dependence take zero values. This indicates the impossibility of predicting the values of one indicator when fixing too small or too large values of another indicator. This work shows that the relationship between the number of COVID-19 coronavirus infections per 100,000 people and the number of deaths from COVID-19 coronavirus infection per 100,000 people in the regions of the Russian Federation can be represented in the form of a Gaussian copula.

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