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The
Non-monotonicity of Value-at-Risk and the Validity of Risk
Measures over Different Horizons
-- Jonathan Treussard
Value-at-Risk
and Conditional Tail Expectations are central tools of modern risk management.
Being risk measures based on the actual probability distribution, they can eventually
decrease with the investment horizon. But this does not prove that stock investments
become less risky in the long run. Instead, equity-risk increases monotonically
at long horizons. This is apparent from economically motivated risk measures,
which are based on risk-neutral probabilities. ©
2007 IUP . All Rights Reserved.
Estimation
of Probability of Default Using Merton's Option Pricing
Approach: An Empirical Analysis
-- Joshy Jacob and Piyush Gupta
The
Basel II accord emphasizes risk sensitiveness for the capital of commercial banks.
It recommends two methods—Standardized Approach and Internal Rating Based
(IRB) Approach—for the estimation of risk capital requirements. Whereas,
the former approach is based on external credit ratings, the latter uses estimates
of Probability of Default (PD). To assess the appropriateness of these approaches
for risk capital estimation, this study employs the Merton's Option Pricing Model
to estimate the PDs for different firms in India. The authors estimate PDs on
a sample of 67 Indian firms during the period 1998-2004. The results obtained
show that the credit ratings accorded by Indian agencies have poor discriminating
power in terms of the PDs. This finding suggests that the credit ratings may not
accurately lead to a correct assessment of risk capital requirement as prescribed
under the standardized approach. Further, as the yearly PDs for the firms do not
show any significant pattern and exhibit high volatility, the estimates of capital
requirement would also be highly volatile under the IRB approach. Either it is
underestimated or overestimated. However, the results of the study are only tentative
as the PDs estimated using the Merton's model are highly influenced by the volatility
in the equity prices that is not necessarily connected to the probability of default. ©
2007 IUP . All Rights Reserved.
Backtesting
of Value-at-Risk Methods for Fixed Income Security and Equity
Portfolios in Indian Market Conditions
--
Pankaj Ganesh Yawalkar, Prabina Rajib and Prasad Rao
Value-at-Risk
(VaR) has emerged as the primary risk measurement tool for market risk in the
last few years. The Bank of International Settlements(BIS) has suggested banks
to measure their market risk using the Value-at-Risk metrics. There are various
VaR metrics, which give different results for the same dataset and period. Hence,
there is a need to test the effectiveness of these VaR calculation methods. This
paper compares various methods of VaR estimation for Fixed Income Securities (FIS)
and Equity portfolios. The authors have used portfolios based on indices to represent
true portfolios. The indices are the Sensex and the i-Bex. These portfolios have
varying weights of FIS and Equity components thus giving rise to two pure and
nine hybrid portfolios. Taking 500 VaR numbers generated by various methods like
Analytical method, Historical Simulation method and Hull and White Historical
Simulation, backtesting has been carried out for these portfolios, using the generally
accepted backtesting technique like the Basel traffic light test and the Kupiec
tests. The results show that the exceptions are proportionately less at 95% confidence
level than at 99% confidence level. This implies leptokurtosis in the returns
data. Among these three methods, the Analytical method performs better than the
other two methods. The Hull and White method is slightly better than the Historical
Simulation Method; the former produces fewer exceptions than the latter. ©
2007 IUP . All Rights Reserved.
Designing
Longevity Risk Transfers: The Point of View of the Cedant
-- Annamaria Olivieri
This
paper focuses on longevity risk, i.e., the risk coming from the random evolution
of mortality at adult ages. Tools to face such risk when managing life annuities,
namely capital allocation and risk transfers are discussed. With regard to the
latter, taking example from traditional reinsurance arrangements, an Excess of
Loss risk transfer, involving the duration of each annuity in the portfolio, and
Stop-Loss arrangements, linking the counter party's intervention to either assets
backing the portfolio reserve or to annual cash flows, are dealt with. The amounts
of capital required in the different situations are then compared, within a simplified
probabilistic framework. ©
2005 Giornale Dell' Istituto Italiano Degli Attuari. This article was earlier
published in the Giornale Dell' Istituto Italiano Degli Attuari, Volume
48. Reprinted with permission. | 
