Delia Coculescu

Default times, no-arbitrage conditions and changes of probability measures

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.

Hazard processes and martingale hazard processses

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 t is an honest time, providing an explicit expression for the difference. Eventually we provide a solution to another open problem: we show that if t is an arbitrary random (default) time such that its Azemas supermartingale is continuous, then t avoids stopping times.

Endogenous Trading in Credit Default Swaps

We introduce a real options model in order to quantify the moral hazard impact of credit default swap (CDS) positions on the corporate default probabilities. Moral hazard is widely addressed in the insurance literature, where the insured agent may become less cautious about preventing the risk from occurring. Importantly, with CDS the moral hazard problem may be magnified since one can buy multiple protections for the same bond. To illustrate this issue, we consider a firm with the possibility of switching from an investment to another one. An investor can influence the strategic decisions of the firm and can also trade CDS written on the firm. We analyze how the decisions of the investor influence the firm value when he is allowed to trade credit default contracts on the firm’s debt. Our model involves a time-dependent optimal stopping problem, which we study analytically and numerically, using the Longstaff–Schwartz algorithm. We identify the situations where the investor exercises the switching option with a loss, and we measure the impact on the firm’s value and firm’s default probability. Contrary to the common intuition, the investors’ optimal behavior does not systematically consist in buying CDSs and increase the default probabilities. Instead, large indifference zones exist, where no arbitrage profits can be realized. As the number of the CDSs in the position increases to exceed several times the level of a complete insurance, we enter in the zone where arbitrage profits can be made. These are obtained by implementing very aggressive strategies (i.e., increasing substantially the default probability by producing losses to the firm). The profits increase sharply as we exit the indifference zone.