Analytical Solutions to Multi-period Credit Portfolio Management A Macroeconomic Approach

Abstract

In this paper we develop a quantitative framework that allows us to calculate portfolio credit risk metrics analytically under multi-period and multi-credit-state environments. Of particular interest is the calculation of (intra-period and cumulative) expected and unexpected portfolio losses. These closed-form, exact formulas enable us to perform risk-based pricing, portfolio optimisation, risk-concentration analysis, stress and reverse stress-testing in a very precise and efficient way (without having to wait for days, if not weeks, for Monte Carlo methods to handle a multi-period, multi-credit-state set-up). Our innovative approach hinges on dynamic scenario generation using structural macroeconomic models. These forward-looking simulations are then linked to credit and market risk parameters, providing an opportunity to leverage the current wave of investment and developments around stress-testing methods. Moreover, the use of general equilibrium, stochastic macro models to build the scenarios gives us the ability to integrate default and mark-to-market risks under a single, unified multi-period framework. https://www.moodysanalytics.com/-/media/article/2015/2015-21-07-moodys-analytics-risk-perspective-risk-data-management.pdf

In this paper we develop a quantitative framework that allows us to calculate portfolio credit risk metrics analytically under multi-period and multi-credit-state environments. Of particular interest is the calculation of (intra-period and cumulative) expected and unexpected portfolio losses. These closed-form, exact formulas enable us to perform risk-based pricing, portfolio optimisation, risk-concentration analysis, stress and reverse stress-testing in a very precise and efficient way (without having to wait for days, if not weeks, for Monte Carlo methods to handle a multi-period, multi-credit-state set-up). Our innovative approach hinges on dynamic scenario generation using structural macroeconomic models. These forward-looking simulations are then linked to credit and market risk parameters, providing an opportunity to leverage the current wave of investment and developments around stress-testing methods. Moreover, the use of general equilibrium, stochastic macro models to build the scenarios gives us the ability to integrate default and mark-to-market risks under a single, unified multi-period framework. https://www.moodysanalytics.com/-/media/article/2015/2015-21-07-moodys-analytics-risk-perspective-risk-data-management.pdf