Related papers: Ambiguity in defaultable term structure models

The intensity of a default time is obtained by assuming that the default indicator process has an absolutely continuous compensator. Here we drop the assumption of absolute continuity with respect to the Lebesgue measure and only assume…

We consider the problem of modelling the term structure of defaultable bonds, under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of…

The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a…

We model the term structure of the forward default intensity and the default density by using L\'evy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the…

We present a general model for default time, making precise the role of the intensity process, and showing that this process allows for a knowledge of the conditional distribution of the default only "before the default". This lack of…

No-arbitrage models of term structure have the feature that the return on zero-coupon bonds is the sum of the short rate and the product of volatility and market price of risk. Well known models restrict the behavior of the market price of…

We introduce a first theory of price impact in presence of an interest-rates term structure. We explain how one can formulate instantaneous and transient price impact on bonds with different maturities, including a cross price impact that…

The main purpose of this paper is to extend the information-based asset-pricing framework of Brody-Hughston-Macrina to a more general set-up. We include a wider class of models for market information and in contrast to the original paper,…

We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and…

In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian…

In credit risk literature, the existence of an equivalent martingale measure is stipulated as one of the main assumptions in the hazard process model. Here we show by construction the existence of a measure that turns the discounted stock…

To construct a no-arbitrage defaultable bond market, we work on the state price density framework. Using the heat kernel approach (HKA for short) with the killing of a Markov process, we construct a single defaultable bond market that…

We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of…

We consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general…

The utility-based pricing of defaultable bonds in the case of stochastic intensity models of default risk is discussed. The Hamilton-Jacobi- Bellman (HJB) equations for the value functions is derived. A finite difference method is used to…

We establish deterministic necessary and sufficient conditions for the no-arbitrage notions NA ("no arbitrage"), NUPBR ("no unbounded profit with bounded risk") and NFLVR ("no free lunch with vanishing risk") in general diffusion market…

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 to introduce a longevity…

We discuss the no-arbitrage conditions in a general framework for discrete-time models of financial markets with proportional transaction costs and general information structure. We extend the results of Kabanov and al. (2002), Kabanov and…

It is shown that absence of arbitrage opportunity in financial markets is a particular case of existence of uncertainty in decision system. Absence of arbitrage opportunity is considered in the sense of the Arrow-Debreu model of financial…

We develop a version of the fundamental theorem of asset pricing for discrete-time markets with proportional transaction costs and model uncertainty. A robust notion of no-arbitrage of the second kind is defined and shown to be equivalent…