A TRACTABLE MULTIVARIATE DEFAULT MODEL BASED ON A STOCHASTIC TIME-CHANGE

2009 ◽  
Vol 12 (02) ◽  
pp. 227-249 ◽  
Author(s):  
JAN-FREDERIK MAI ◽  
MATTHIAS SCHERER
Keyword(s):  
Full Range ◽  
Time Change ◽  
Dependence Structure ◽  
Arbitrary Distribution ◽  
Risky Assets ◽  
Portfolio Loss Distribution ◽  
Two Parameters ◽  
Portfolio Loss ◽  
Stochastic Time ◽  
Lévy Subordinators

A stochastic time-change is applied to introduce dependence to a portfolio of credit-risky assets whose default times are modeled as random variables with arbitrary distribution. The dependence structure of the vector of default times is completely separated from its marginal default probabilities, making the model analytically tractable. This separation is achieved by restricting the time-change to suitable Lévy subordinators which preserve the marginal distributions. Jump times of the Lévy subordinator are interpreted as times of excess default clustering. Relevant for practical implementations is that the parameters of the time-change allow for an intuitive economical explanation and can be calibrated independently of the marginal default probabilities. On a theoretical level, a so-called time normalization allows to compute the resulting copula of the default times. Moreover, the exact portfolio-loss distribution and an approximation for large portfolios under a homogeneous portfolio assumption are derived. Given these results, the pricing of complex portfolio derivatives is possible in closed-form. Three different implementations of the model are proposed, including a compound Poisson subordinator, a Gamma subordinator, and an Inverse Gaussian subordinator. Using two parameters to adjust the dependence structure in each case, the model is capable of capturing the full range of dependence patterns from independence to complete comonotonicity. A simultaneous calibration to portfolio-CDS spreads and CDO tranche spreads is carried out to demonstrate the model's applicability.

scholarly journals REGULATORY CAPITAL MODELING FOR CREDIT RISK

2015 ◽  
Vol 18 (05) ◽  
pp. 1550034 ◽  
Author(s):  
MAREK RUTKOWSKI ◽  
SILVIO TARCA
Keyword(s):  
Credit Risk ◽  
Banking Sector ◽  
General Setting ◽  
Capital Adequacy ◽  
Dependence Structure ◽  
Regulatory Capital ◽  
Loss Distribution ◽  
Portfolio Loss Distribution ◽  
Portfolio Loss ◽  
Irb Approach

The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk plays an important role in protecting the banking sector against insolvency. We outline the mathematical foundations of regulatory capital for credit risk, and extend the model specification of the IRB approach to a more general setting than the usual Gaussian case. It rests on the proposition that quantiles of the distribution of conditional expectation of portfolio percentage loss may be substituted for quantiles of the portfolio loss distribution. We present a more compact proof of this proposition under weaker assumptions. Then, constructing a portfolio that is representative of credit exposures of the Australian banking sector, we measure the rate of convergence, in terms of number of obligors, of empirical loss distributions to the asymptotic (infinitely fine-grained) portfolio loss distribution. Moreover, we evaluate the sensitivity of credit risk capital to dependence structure as modeled by asset correlations and elliptical copulas. Access to internal bank data collected by the prudential regulator distinguishes our research from other empirical studies on the IRB approach.

Commodity Forward Curves With Stochastic Time Change

2021 ◽  
Author(s):  
Sergiy Ladokhin ◽  
Maren Diane Schmeck ◽  
Svetlana Borovkova
Keyword(s):  
Time Change ◽  
Stochastic Time

scholarly journals Electricity price modeling with stochastic time change

2017 ◽  
Vol 63 ◽  
pp. 51-65 ◽  
Author(s):  
Svetlana Borovkova ◽  
Maren Diane Schmeck
Keyword(s):  
Time Change ◽  
Electricity Price ◽  
Stochastic Time

The magnetohydrodynamic flow past a flat plate

1959 ◽  
Vol 6 (1) ◽  
pp. 77-96 ◽  
Author(s):  
H. P. Greenspan ◽  
G. F. Carrier
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Field ◽  
Flat Plate ◽  
Steady Flow ◽  
Full Range ◽  
Ambient Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Two Parameters

The uniform steady flow of an incompressible, viscous, electrically conducting fluid is distorted by the presence of a symmetrically oriented semi-infinite flat plate. The ambient magnetic field is coincident with the ambient velocity field. The description of the resulting fields depends on the physical co-ordinates measured in units of Reynolds number and on the two parameters ε = ωμν and β = μH2/ρv2. This description of the fields is approximated in three different ways and essentially covers the full range of ε and β. In particular, when β [Gt ] 1, no steady flow which is uniform at large distances from the plate exists.

Macroeconomic shocks and credit risk stress testing the Iranian banking sector

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fatemeh Abdolshah ◽  
Saeed Moshiri ◽  
Andrew Worthington
Keyword(s):  
Banking Sector ◽  
Nonlinear Models ◽  
Economic Capital ◽  
Macroeconomic Shocks ◽  
Loss Distribution ◽  
Content Type ◽  
Macroeconomic Conditions ◽  
Linear And Nonlinear ◽  
Portfolio Loss Distribution ◽  
Portfolio Loss

PurposeThe Iranian banking industry has been greatly affected by dramatic changes in macroeconomic conditions over the past several decades owing to volatile oil revenues, changing fiscal and monetary policies, and the imposition of US sanctions. The main objective of this paper is to estimate potential credit losses in the Iranian banking sector due to macroeconomic shocks and assess the minimum economic capital requirements under the baseline and distressed scenarios. The paper also contrasts the applications of linear and nonlinear models in estimating the impacts of macroeconomic shocks on financial institutions.Design/methodology/approachThe paper uses a multistage approach to derive the portfolio loss distribution for banks. In the first step, the dynamic relationship between the selected macroeconomic variables are estimated using a VAR model to generate the stress scenarios. In the second step, the default probabilities are estimated using a quantile regression model and the results are compared with those of the conventional linear models. Finally, the default probabilities are simulated for a one-year time horizon using Monte-Carlo method and the portfolio loss distribution is calculated for hypothetical portfolios. The expected loss includes the loss given default for loans drawn randomly and uniformly distributed and exposed at default values when loans are assigned a fixed value.FindingsThe results indicate that the loss distributions under all scenarios are skewed to the right, with the linear model results being very similar to those of quantile at the 50% quantile, but very unlike those at the 10% and 90% quantiles. Specifically, the quantile model for the 90% (10%) quantile generates estimates of minimum economic capital requirement that are considerably higher (lower) than those using the linear model.Research limitations/implicationsThe study has focused on credit risk because of lack of data on other types of risk at individual bank level. The future studies can estimate the aggregate economic capital using a risk aggregation approach and a panel data (not presently available), which could further improve the accuracy of the estimates.Practical implicationsThe fiscal and monetary authorities in developing countries, specially oil-exporting countries, can follow the risk assessment approach to assess the health of their banking system and adapt policies to mitigate the impacts of large macroeconomic shocks on their financial markets.Originality/valueThis is the first paper estimating the portfolio loss distribution for the Iranian banks under turbulent macroeconomic conditions using linear and nonlinear models. The case study can be applied to other developing and emerging countries, particularly those highly dependent on natural resources, prone to extreme macroeconomic shocks.

scholarly journals Asset correlation, portfolio diversification and regulatory capital in the Basel Capital Accord

2011 ◽  
Vol 1 (3) ◽  
pp. 31-39 ◽  
Author(s):  
Sylvia Gottschalk
Keyword(s):  
Basel Ii ◽  
Capital Adequacy ◽  
Probability Of Default ◽  
Regulatory Capital ◽  
Kmv Model ◽  
High Quantiles ◽  
Portfolio Loss Distribution ◽  
Credit Portfolio ◽  
Portfolio Loss ◽  
Asset Correlation

In this paper, we analyze the properties of the KMV model of credit portfolio loss. This theoretical model constitutes the cornerstone of Basel II’s Internal Ratings Based(IRB) approach to regulatory capital. Our results show that this model tends to overestimate the probability of portfolio loss when the probability of default of a single firm and the firms’ asset correlations are low. On the contrary, probabilities of portfolio loss are underestimated when the probability of default of a single firm and asset correlations are high. Moreover, the relationship between asset correlation and probability of loan portfolio loss is only consistent at very high quantiles of the portfolio loss distribution. These are precisely those adopted by the Basel II Capital Accord for the calculations of capital adequacy provisions. So, although the counterintuitive properties of the KMV model do not extend to Basel II, they do restrict its generality as a model of credit portfolio loss.

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