Credit Cycle-dependent Stochastic Credit Spreads and Rating Category Transitions

Terry Benzschawel

This article was first published as a chapter in Credit Modelling (2nd edition), by Risk Books.

This chapter will present a method for calculating value at risk (VaR) for corporate bonds using simulation methods. The simulations involve adjusting historical credit-state transition matrices for changes in default rates, ratings upgrades and downgrades, and credit spread changes as they occur over the credit-cycle dependant credit state. Transition matrices are constructed at monthly intervals out to one year, and annually out to five years thereafter. Average physical default probabilities were obtained by rating and tenor from the market-implied PD model of Benzschawel and Assing (2012), and ratings from one to five years were generated stochastically based on historical patterns of observed default rates. The time series of credit-state transition matrices were generated by inferring ratings upgrades and downgrade from estimates of the existing overall default rate referenced to historical upgrade/downgrade ratios. These economic cycle-adjusted transition matrices can be used to infer likelihoods of transitioning among various credit states given market conditions.

Given the