Credit Risk and Incomplete Information: Filtering and Em Parameter Estimation

Abstract

We consider a reduced-form credit risk model where default intensities and interest rate are functions of a not fully observable Markovian factor process, thereby introducing an information-driven default contagion effect among defaults of different issuers. We determine arbitrage-free prices of OTC products coherently with information from the financial market, in particular yields and credit spreads and this can be accomplished via a filtering approach coupled with an EM-algorithm for parameter estimation.

A unified approach to pricing and risk management of equity and credit risk

“…The process Y can include macro-economic covariates describing the state of the economy as well as firmspecific and latent variables, as considered e.g. in [19,20]. Let us define the process L = (L t ) 0≤t≤T by L t := logS t and the…”

Mathematical and Statistical Methods for Actuarial Sciences and Finance

“…It is clear that P D m (t, T ) and F (t, T ) are by construction coherent with the observed default-free and defaultable term structures and also with the rating-based information, due to the definition of Y t . Furthermore, since r t is assumed to be (Y t ) t -adapted, it can be easily shown that (10b) defines an arbitrage-free price system in the investors' filtration (Y t ) t (see [14], Lemma 6).…”

“…We aim at extending the modeling approach originally proposed in [14], in order to cover not only applications to pricing but also to risk management. This raises the need to formulate the model under both the physical and the risk-neutral probability measures, which are linked via the risk premium process.…”

“…Since the latter is not fully observable, a filtering procedure is proposed in order to dynamically update the information on the unobserved factors on the basis of publicly available information. Such information consists not only of market data (the interest rate, yields on default-free bonds and credit spreads on defaultable bonds) but also of the information coming from the rating scores, thereby extending the filtering methodology presented in [14]. Indeed, as pointed out in [15], credit ratings contain important information not captured by credit spreads about corporate defaults and can also be regarded as noisy measures of actual default probabilities (see also [9,13], Chap.…”

“…Section 4 describes the structure of the information actually available to the investors and, finally, Section 5 deals with the formulation and (an outline of) the solution of the filtering problem. We refer the reader to [14] for a thorough analysis of the parameter estimation problem, which turns out to be deeply linked to the filtering problem, and for a numerical study of the main features of the proposed algorithm.…”