An Infinite Factor Model for Credit Risk

Abstract

The defaultable term structure is modeled using stochastic differential equations in Hilbert spaces. This leads to an infinite dimensional model, which is free of arbitrage under a certain drift condition. Furthermore, the model is extended to incorporate ratings based on a Markov chain.

Volatility estimation for stochastic PDEs using high-frequency observations

“…The neat representation (6) separates dependence on time and space and connects the SPDE model to stochastic processes in Hilbert spaces. This structure has been exploited in several works, especially for financial applications, see, for instance, Bagchi and Kumar (2001) and Schmidt (2006). We consider the following observation scheme.…”

Factor Copula Models and Their Application in Studying the Dependence of the Exchange Rate Returns

“…As Schmidt (2006) outlined in his work, Gaussian copulas are an extension from the multivariate normal distribution. Let us assume that X 1 and X 2 are normally distributed and they are also jointly normal.…”

General Dynamic Term Structures Under Default Risk

“…Accordingly, reduced-form HJM-type models for defaultable term structures typically postulate that, prior to default, bond prices are absolutely continuous with respect to maturity, i.e., under the assumption of zero recovery, credit risky bond prices P pt, T q are described by (1.1) P pt, T q " 1 tτ ątu expˆ´ż T t f pt, uqdu˙, with τ denoting the random default time and pf pt, T qq 0ďtďT an instantaneous forward rate. This approach has been studied in numerous works and up to a great level of generality, beginning with the first works [13,36,50,51] and extended in various directions in [15,16,45,49] (see [4,Chapter 13] for an overview of the relevant literature). It turns out that, assuming absence of arbitrage, the presence of predictable times at which the default event can occur with strictly positive probability is incompatible with an absolutely continuous term structure of the form (1.1).…”