Diana Dorobantu

Optimal strategies in a risky debt context

This paper analyses structural models for the evaluation of risky debt following Leland (J. Finance 49 (1994), pp. 1213–1252) with an approach of optimal stopping problem. Moreover, we introduce an investment control parameter and we optimize with respect to the failure threshold and coupon rate. We show that the value of the optimal coupon policy decreases if the strict priority rule is removed.

First passage time law for some Lévy processes with compound Poisson : existence of a density

Let (Xt, t >= 0) be a diffusion process with jumps, sum of a Brownian motion with drift and a compound Poisson process. We consider T_x the first hitting time of a fixed level x > 0 by (Xt, t >= 0). We prove that the law of T_x has a density (defective when E(X1) < 0) with respect to the Lebesgue measure.Let (Xt, t >= 0) be a diffusion process with jumps, sum of a Brownian motion with drift and a compound Poisson process. We consider T_x the first hitting time of a fixed level x > 0 by (Xt, t >= 0). We prove that the law of T_x has a density (defective when E(X1) < 0) with respect to the Lebesgue measure.

Risk assessment using suprema data

This paper proposes a stochastic approach to model temperature dynamic and study related risk measures. The dynamic of temperatures can be modelled by a mean-reverting process such as an Ornstein–Uhlenbeck one. In this study, we estimate the parameters of this process thanks to daily observed suprema of temperatures, which are the only data gathered by some weather stations. The expression of the cumulative distribution function of the supremum is obtained thanks to the law of the hitting time. The parameters are estimated by a least square method quantiles based on this function. Theoretical results, including mixing property and consistency of model parameters estimation, are provided. The parameters estimation is assessed on simulated data and performed on real ones. Numerical illustrations are given for both data. This estimation will allow us to estimate risk measures, such as the probability of heat wave and the mean duration of an heat wave.

Valuation of portfolio loss derivatives in an infectious model

In this paper we investigate a dynamic credit risk contagion model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). The spontaneous default without external influence and the infections are described by conditionally independent Bernoulli-type random variables. We provide a recursive algorithm for the computation of the loss distribution that involves successive applications of the so-called Waring’s formula. The major advantage of this algorithm is that it can be applied for a large portfolio. We then examine the calibration of model parameters on CDX.NA.IG tranche quotes during the crisis.

Risky debt and optimal coupon policy and other optimal strategies

AbstractThe model developed is a structural valuation model of risky debt which includes a dynamic of debt. The value of the firm follows either a Brownian dynamic or a mixed Brownian-Poisson dynamic. The default threshold is endogenous; thus the optimal default threshold changes as the firms value changes. Another optimal control problem is setting with respect to a couple (coupon or dividend policy, stopping time). Hence a local time is introduced in the firm value dynamic, being the optimal coupon or dividend policy. Once again an optimal threshold is given.