Obtaining the distribution of the profit and loss (PL) of a portfolio is a key problem in market risk measurement. However, existing methods, such as those based on the Normal distribution, and historical simulation methods, which use empirical distribution of risk factors, face difficulties in...

This paper aims to extract the expectations of market participants on the duration of the Zero Interest Rate Policy (ZIRP) by the Bank of Japan by modeling the term structure of interest rates. Under the ZIRP, particularly the short-term and medium-term interest rates are so low that we face...

In this study, we derive an analytical solution for the expected loss and the higher moment of the discounted loss distribution for a collateralized loan. To ensure non-negative values for the intensity and interest rate, we assume a quadratic Gaussian process for the default intensity and...

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...

In this study, we derive an analytical solution for expected loss and the higher moment of the discounted loss distribution for a collateralized loan. To ensure nonnegative values for intensity and interest rate, we assume a quadratic Gaussian process for default intensity and discount interest...

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>