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Basel II Second Pillar: An Analytical VaR
with Contagion and Sectorial Risks
--Michele Bonollo, Paola Mosconi and Fabio Mercurio
This paper deals with the effects of concentration (single name and sectoral) and contagion risk on credit portfolios.
Results are obtained for the Value at Risk (VaR) of the portfolio loss distribution, in the analytical framework originally developed
by Vasicek in 1991. VaR is expressed as a sum of terms—the first contribution represents the VaR of a hypothetical
single-factor homogeneous portfolio, the remaining terms are corrections due to contagion, imperfect granularity and multiple
industry-geographic sectors. A detailed numerical analysis is also presented.
© 2010 IUP. All Rights Reserved.
Migration Analysis of Indian Corporate:
Rating-Based Approach
--Richa Verma Bajaj
Implementation of Basel II has made it compulsory for banks to study the transition and default in their rating grades to
judge the quality of their credit portfolio. In the similar direction, the present study is undertaken primarily to view the
migration and default rate conditional on rating of the long-term debt issuers and macroeconomic fundamentals for the period
from January 1994 to January 2009. The CRISIL's annual ratings of debts issued by 578 corporate (Manufacturing
Companies) formed the basis of the analysis. It is found from the analysis that the least stable retention rate was found in low rating
grade issuers. The mortality (default) rate was observed low for high rated issuer and high for low rated ones. The analysis
clearly indicates that the ratings transition is cyclical in nature and so the default probability.
© 2010 IUP. All Rights Reserved.
Assessing the Quality of Retail Customers:
Credit Risk Scoring Models
--Gabriele Sabato
Credit scoring models play a fundamental role in the risk management practice of most banks. They are used to quantify
credit risk at counterparty or transaction level in the different phases of the credit cycle (e.g., application, behavioral and
collection models). The credit score empowers users to make quick decisions or even to automate decisions and this is extremely
desirable when banks are dealing with large volumes of clients and relatively small margin of profits at individual transaction level
(i.e., consumer lending, but also increasingly small business lending). This paper analyzes the history and new developments
related to credit scoring models. It is found that with the New Basel Capital Accord, credit scoring models have been remotivated
and given unprecedented significance. Banks, in particular, and most financial institutions, worldwide, have either recently developed
or modified their existing internal credit risk models to conform with the new rules and best practices recently updated in
the market. Moreover, the key steps of the credit scoring model's lifecycle (i.e., assessment, implementation and
validation) highlighting the main requirement imposed by Basel II have also been analyzed. It is concluded that banks that are willing
to implement the most advanced approach to calculate their capital requirements under Basel II will need to increase their
attention and consideration of credit scoring models in the near future.
© 2010 IUP. All Rights Reserved.
An Alternative Threshold-GARCH
Option Pricing Model
--Shu-Ing Liu
This paper proposes an alternative Threshold-GARCH (TGARCH) option pricing model, which is a modification of
the TGARCH model introduced by Härdle and Hafner (2000). Some moment properties of the proposed model are
analytically proven. Parameter estimations are analyzed by the Bayesian approach via suitable Markov Chain Monte-Carlo
(MCMC) techniques. Numerical illustrations are presented using a few S&P 100 and 500 stock index series and related call option
price series. The posterior inference results indicate that the threshold effects on the volatility structure are significant.
Moreover, the out-of-sample forecasting results also reveal that the inclusion of the threshold effect indeed enhances the forecasting
ability, especially, in the case of the out-of-the-money S&P 100 call option.
© 2010 IUP. All Rights Reserved.
A Risk Contribution Approach
to Asset Allocation
--Claudio Boido and Giovanni Fulci
The aim of this paper is to verify whether efficient portfolios, obtained using traditional tools of asset allocation, provide
real diversification of risk, in addition to the division of capital into different asset classes. It is shown how portfolios that
seem diversified in their capital allocation are too heavily concentrated in terms of risk allocation. To solve this problem, use of
a risk budgeting approach based on equal marginal contributions to total risk is proposed. By using this approach the
dispersion of risk is maximized, effectively reducing the intensity and the length of drawdowns and diversifying their source, with
equal volatility as that of a traditional portfolio.
© 2010 IUP. All Rights Reserved.
Multidimensional Extension of the Archimedean Copula
for Financial Return Modeling
--Woohwan Kim
This paper proposes two nested methods—fully nested and partially nested—for the general
d-dimensional extension of the Archimedean copula. It has extensively been used to model dependence among the return
series, however, its extension to general d-dimension with a proper dependence structure is limited. The paper analyzes the data
of six major stock indices collected on a daily basis for the period, March 8, 2002 to March 7, 2007, and finds that
partially nested structure is better than a symmetric and fully nested structure for general empirical application. Kendall's tau has
been primarily used for determining a nested structure owing to its one-to-one relationship with the Archimedean copula
parameter. The paper quantifies the impact of the dependence structure on portfolio risk measured by Value at Risk (VaR) and
conducts a backtest for assessing the soundness of the VaR models. It confirms that the dependence structure of the return series is
a critical determinant of the portfolio VaR and partially nested structure gives a conservative VaR estimate in comparison to
the symmetric case.
© 2010 IUP. All Rights Reserved.
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