A Short Note on Market-Consistent Calibration of Static Recovery Rates

Abstract

The elephant in the room around CDS, CMBS, CMBX, and CDO pricing is the recovery rate. Practically, whilst recovery swaps exist they are not liquid. The problem is especially acute when upfront payments, or quoted prices, contradict previous recovery rate assumptions, e.g. pre-crisis, 40% for equities, or up to 80% (or more) for some CMBS. Although recoveries will decrease as rating drop, ratings are not always in sync with market movements. This is exacerbated when CDS-on-CMBS are considered, either with pay-as-you-go CDS, or (for tranches thinner than one commercial mortgage) standard CDS. Theoretical developments have run ahead of market reality for calibration. Whilst CDS and CDO reduced-form models exist for stochastic hazard rates and stochastic recovery rates actual calibration is problematic. In this paper we take a step backwards and consider a dynamic calibration of traditional static CDS models to market data. We start from the usual daily model recalibration and propose heuristics for market-consistent calibration of static data, specifically the recovery rate within static hazard rate models. These are based on strong constraints on recovery rates from observed CDS prices. Note that this static approach is complementary to the dynamic RMV and is advantageous in that standard CDS and CDO pricing is unchanged. These heuristics can be extended and generalized in different ways within stochastic models. For example the market-implied recovery rate that is now an output can be the input for a stochastic recovery rate model e.g. Charaf08,Yadong09,Werpachowski09 (all on SSRN).