We compare expected shortfall and value-at-risk (VaR) in terms of consistency with expected utility maximization and elimination of tail risk. We use the concept of stochastic dominance in studying these two aspects of risk measures. We conclude that expected shortfall is more applicable than...

We compare expected shortfall with value-at-risk (VaR) in three aspects: estimation errors, decomposition into risk factors, and optimization. We describe the advantages and the disadvantages of expected shortfall over VaR. We show that expected shortfall is easily decomposed and optimized while...

We evaluate expected and unexpected losses of a bank loan, taking into account the bankfs strategic control of the expected return on the loan. Assuming that the bank supplies an additional loan to minimize the expected loss of the total loan, we provide analytical formulations for expected and...

Valuation of the conversion option is essential in analyzing the market price of a convertible bond. In this paper, we use a binomial tree pricing model to derive the implied volatility of the conversion option from the past price information (time-series data for individual issues) in the...

The common practice for managing the credit risk of lending portfolios is to the calculate the maximum loss within the "value at risk" framework. Most financial institutions use large-scale Monte Carlo simulations to do this. However, such simulations may impose heavy calculation loads. This...

Value-at-risk (VaR) has become a standard measure used in financial risk management due to its conceptual simplicity, computational facility, and ready applicability. However, many authors claim that VaR has several conceptual problems. Artzner et al. (1997, 1999), for example, have cited the...

In this paper, we compare value-at-risk (VaR) and expected shortfall under market stress. Assuming that the multivariate extreme value distribution represents asset returns under market stress, we simulate asset returns with this distribution. With these simulated asset returns, we examine...

This paper surveys several applications of parametric copulas to market portfolios, credit portfolios, and enterprise risk management in the banking industry, focusing on how to capture stressed conditions. First, we show two simple applications for market portfolios: correlation structures for...

<Para ID="Par1">We evaluate the expected loss and the standard deviation of loss of a bank loan, considering the bank’s strategic control of the expected return on the loan. Assuming that the bank supplies an additional loan to minimize the expected loss of the total loan, we provide analytical formulations...</para>

This paper examines the marginal distributions of stocks and bonds, and a copula between the movement of stock prices and interest rates. Because some widely used aggregation methods such as variance-covariance tend to underestimate the risk of an aggregated portfolio, a copula is utilized for...