Analytical Framework for Credit Portfolios. Part I: Systematic Risk

TL;DR

This paper introduces an analytical framework for calculating systematic risk metrics in credit portfolios, eliminating the need for Monte Carlo simulations and enabling precise risk attribution at the transaction level.

Contribution

It presents a novel analytical method for credit portfolio risk measurement based on a multi-factor Merton model, improving efficiency and accuracy over traditional simulation approaches.

Findings

High accuracy demonstrated through benchmarking against Monte Carlo simulations

Framework enables calculation of standard deviation, VaR, and Expected Shortfall analytically

Risk allocation can be performed at the individual transaction level

Abstract

Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures (standard deviation, VaR and Expected Shortfall) as well as allocation of risk down to individual transactions. The underlying model is the industry standard multi-factor Merton-type model with arbitrary valuation function at horizon (in contrast to the simplistic default-only case). High accuracy of the proposed analytical technique is demonstrated by benchmarking against Monte Carlo simulations.