Chapter 7 - Stable modeling of market and credit value at risk

Abstract

This chapter examines the use of stable Paretian distributions in modeling market and credit value at risk (VaR). The in-sample and forecast evaluations highlight the fact that stable market VaR modeling outperforms the “normal” modeling for high values of the VaR confidence level. The chapter also develops a new technique for estimating correlation, constructs a new method for simulating portfolio values, and assesses portfolio VaR in various cases of credit instruments distributions: independent, symmetric dependent, and skewed dependent. One of the most important tasks of financial institutions is evaluating the exposure to market and credit risks. Market risks arise from variations in prices of equities, commodities, exchange rates, and interest rates. Credit risks refer to potential losses that might occur because of a change in the counterparty's credit quality, such as a rating migration or a default. The dependence on market and credit risks is measured by changes in the portfolio value, or profits, and losses. The essence of the VaR computations is estimation of low quantiles in the portfolio return distributions. The VaR techniques suggest different ways of constructing the portfolio return distributions. The traditional methods are the parametric method, historical simulation, Monte Carlo simulation, and stress testing.