Sous le titre Mythen und Realitäten, Steffen Lau et Josef Sachs ont récemment revisité la question du secret médical dans la prise en charge de détenus dangereux. Leur intention était de recentrer le débat sur la réalité de la psychiatrie forensique en réponse au discours «émotionnel» qui, selon eux, prédomine en Suisse romande. Malheureusement, loin de combattre les mythes, l’article ne fait que les accentuer tout en prenant quelques libertés avec le cadre légal de la pratique médicale en prison.
We propose a valuation method for financial assets subject to default risk, where investors cannot observe the state variable triggering the default but observe a correlated price process. The model is sufficiently general to encompass a large class of structural models and can be seen as a generalization of the model of Duffie and Lando (Econometrica 69:633–664, [2001]). In this setting we prove that the default time is totally inaccessible in the market’s filtration and derive the conditional default probabilities and the intensity process. Finally, we provide pricing formulas for default-sensitive claims and illustrate in particular examples the shapes of the credit spreads.
The occurrence of some events can impact asset prices and produce losses. The amplitude of these losses are partly determined by the degree of predictability of those events by the market investors, as risk premiums build up in an asset price as a compensation of the anticipated losses. The aim of this paper is to propose a general framework where these phenomena can be properly defined and quantified.
Our focus are the default events and the defaultable assets, but the framework could apply to any event whose occurrence impacts some asset prices.
We provide the general construction of a default time under the so called (H) hypothesis, which reveals a useful way in which default models can be built, using both market factors and idiosyncratic factors. All the relevant characteristics of a default time (i.e. the Azema supermartingale and its Doob-Meyer decomposition) are explicitly computed given the information about these factors.
We then define the default event risk premiums and the default adjusted probability measure. These concepts are useful for pricing defaultable claims in a framework that includes possible economic shocks, such as jumps of the recovery process or of some default-free assets at the default time. These formulas are not classic and we point out that the knowledge of the default compensator (or the intensity process when the default time is totally inaccessible) is not a sufficient quantity for finding explicit prices; the Azema supermartingale and its Doob-Meyer decomposition are needed. The progressive enlargement of a filtration framework is the right tool for pricing defaultable claims in non standard frameworks where non defaultable assets or recovery processes may react at the default event.
This study provides new insights on how investors form beliefs about future asset prices and how they use these beliefs for their trading decisions. Compared to the objective Bayesian benchmark, investors become overly optimistic when they face a paper loss. In addition, selling decisions are less sensitive to beliefs than purchase decisions. This difference is driven by selling behavior in the presence of paper losses. Our insights stem from a laboratory experiment in which participants are price-takers and trade a stock governed by a persistent two-state Markov chain. At each point in time, we elicit incentivized beliefs about the probability that the stock price will increase in the next period.
In this paper, we give a financial justification, based on no-arbitrage conditions, of the (H)-hypothesis in default time modeling. We also show how the (H)-hypothesis is affected by an equivalent change of probability measure. The main technique used here is the theory of progressive enlargements of filtrations.
We build a general model for pricing defaultable claims. In addition to the usual absence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when the default occurs. We prove that under this assumption, in some standard market filtrations, default times are totally inaccessible stopping times; we therefore proceed to a systematic construction of default times with particular emphasis on totally inaccessible stopping times. Surprisingly, this abstract mathematical construction, reveals a very specific and useful way in which default models can be built, using both market factors and idiosyncratic factors. We then provide all the relevant characteristics of a default time (i.e. the Az\'ema supermartingale and its Doob-Meyer decomposition) given the information about these factors. We also provide explicit formulas for the prices of defaultable claims and analyze the risk premiums that form in the market in anticipation of losses which occur at the default event. The usual reduced-form framework is extended in order to include possible economic shocks, in particular jumps of the recovery process at the default time. This formulas are not classic and we point out that the knowledge of the default compensator or the intensity process is not anymore a sufficient quantity for finding explicit prices, but we need indeed the Az\'ema supermartingale and its Doob-Meyer decomposition.
In this article, we define the notion of a filtration and the related notion of the usual hypotheses. We then explain the problem of enlargements of filtrations: how are (semi)martingales affected under a change of filtrations? We state the main theorems in the classical frameworks of initial and progressive enlargements of filtrations. In the case of initial enlargements of filtrations, we state the well known Jacod's condition and in the framework of progressive enlargements of filtrations, we give the decomposition of a local martingale in the larger filtration. We finally specialize to the case of immersed filtrations, which is very widely used in credit risk modeling, and study the effect of a combination of changes of filtration and probability measure in this situation.
In this paper we model the situation where a non-renewable investment is given, for instance a resource reservoir, and show how to optimally trade-off between dividends and leverage, in order to maximize a performance indicator for shareholders, up to the bankruptcy time. We then study the way market risk (the volatility of the market price of the resource) impacts the optimal policies and the default risk of the company. The moments when the policies are rebalanced are analyzed and we give a measure of the agency costs which appear between the shareholders and the debt-holders.
In this paper, we build a bridge between different reduced-form approaches to pricing defaultable claims. In particular, we show how the well-known formulas by Duffie, Schroder, and Skiadas and by Elliott, Jeanblanc, and Yor are related. Moreover, in the spirit of Collin Dufresne, Hugonnier, and Goldstein, we propose a simple pricing formula under an equivalent change of measure.
Two processes will play a central role: the hazard process and the martingale hazard process attached to a default time. The crucial step is to understand the difference between them, which has been an open question in the literature so far. We show that pseudo-stopping times appear as the most general class of random times for which these two processes are equal. We also show that these two processes always differ when $\tau$ is an honest time, providing an explicit expression for the difference. Eventually we provide a solution to another open problem: we show that if $\tau$ is an arbitrary random (default) time such that its Azéma's supermartingale is continuous, then $\tau$ avoids stopping times.
