Estimating default probabilities using a non parametric approach

Estimation of Default Probabilities is critical to the correct pricing of credit derivatives and determining the appropriate level of reserves to support credit risky activities (Basel II). Given that credit default swaps (CDS) reflect the market consensus on default probability (with a direct mapping between the two), much research has focused on modelling observable credit spreads as surrogates for default probabilities. Many credit spread models are parametric, causing model error and parameter estimation error.Working in a Merton (1974) type framework, we first consider the equity -- credit link.Having established that equity and bond prices are positively correleated when debt to asset ratios are high, and that prices in the CDS, bond and equity markets adjust simultaneously when there is new information on credit risk, we simulate alternative equity price paths to assess how credit default spreads may have evolved differently from the historical record. While historically a firm may not have defaulted, financial distress may have occurred if the evolution of the equity prices had differed. By simulation of multiple alternative equity price paths, we aim to assess credit default spreads that could have associated with increased default probabilities. This entails the use of a non-parametric simulation approach, suggested by Tompkins and D'Ecclesia (2005) which both matches facets of the empirical stock price path and provides simultations with exactly the same statistical features as the historical record with alternative paths. We determine standardised disturbances from the unconditional historical equity return series and by mixing these disturbances, generate alternative price paths. Such an approach does not require the assumption of normality in the underlying equity return series. However, it is assumed that the relationship between equity prices and credit default swaps is stationary. Using this relationship and the non parametric simulation approach we estimate the default probabilities