Default Ambiguity

Abstract

This paper discusses ambiguity in the context of single-name credit risk. We focus on uncertainty in the default intensity but also discuss uncertainty in the recovery in a fractional recovery of the market value. This approach is a first step towards integrating uncertainty in credit-risky term structure models and can profit from its simplicity. We derive drift conditions in a Heath–Jarrow–Morton forward rate setting in the case of ambiguous default intensity in combination with zero recovery, and in the case of ambiguous fractional recovery of the market value.

Reduced-form setting under model uncertainty with non-linear affine intensities

“…F Here, we wish to provide the most general reduced-form setting under model uncertainty which allows numerical tractability or explicit computation for pricing insurance liabilities or credit derivatives. Hence, we extend the results in [5] by representing the mortality intensity as non-linear affine processes in the sense of [15]. By doing so we are able to construct a general market model, where the risky assets are local -martingales and the intensity process is a non-linear affine process under the considered (time-dependent increasing) families of probability measures.…”

“…In this setting no specific structure or assumptions are made for the intensity process. In the last few years several papers dealing with short rate modeling under model uncertainty have been published, e.g., [22−24], [16], and [15]. A more general approach is treated in [15] by considering affine processes under parameter uncertainty, called non-linear affine processes, as an extension of the non-linear Lévy processes in [34].…”

“…In the last few years several papers dealing with short rate modeling under model uncertainty have been published, e.g., [22−24], [16], and [15]. A more general approach is treated in [15] by considering affine processes under parameter uncertainty, called non-linear affine processes, as an extension of the non-linear Lévy processes in [34]. More specifically, one-dimensional non-linear affine processes are defined as a family of semimartingale laws whose differential characteristics are bounded from above and below by affine functions of the current states.…”

“…Aim of this paper is to extend the reduced-form setting under model uncertainty as introduced in [5] to include non-linear affine intensities as defined in [15]. In this way, we introduce a longevity bond under model uncertainty in an arbitrage-free way and numerically compute its value process in several examples.…”

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In this paper we extend the reduced-form setting under model uncertainty introduced in [5] to include intensities following an affine process under parameter uncertainty, as defined in [15]. This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically.

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