Forward equations for option prices in semimartingale models

We derive a forward partial integro-differential equation for prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by a -possibly discontinuous- semimartingale. This result generalizes Dupire's forward equation to a large class of non-Markovian models with jumps and allows to retrieve various forward equations previously obtained for option prices in a unified framework.

Forward equations for option prices in semimartingale models

We derive a forward partial integro-differential equation for prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by a -possibly discontinuous- semimartingale. This result generalizes Dupire's forward equation to a large class of non-Markovian models with jumps and allows to retrieve various forward equations previously obtained for option prices in a unified framework.

Time to AIDS from 1992 to 1999 in HIV-1-Infected Subjects with Known Date of Infection.

To estimate the change in AIDS incubation time during three periods characterized by different availability of antiretroviral treatments, data from the French Hospital Database on HIV of 4702 HIV-1-positive subjects with a documented date of infection were analyzed. Times from seroconversion to AIDS were compared in three periods: period 1 from January 1992 to June 1995 (monotherapy); period 2 from July 1995 to June 1996 (dual therapy); and period 3 from July 1996 to June 1999 (triple therapy). Nonparametric survival analyses were performed to account for staggered entries in the database and during each period. From periods 1 to 3, antiretroviral treatments were initiated earlier after infection, more subjects were treated, and the nature of regimens changed (25.6% of subjects were treated with monotherapy in period 1, 34.6% were treated with dual therapy in period 2, and 53.4% were treated with triple therapy in period 3). Compared with period 1, the relative hazard (RH) of AIDS was 0.31 in period 3 (95% confidence interval [CI]: 0.24-0.39). When comparing period 3 with period 2, the RH of AIDS was 0.36 (CI: 0.29-0.45). Assuming a log normal distribution, the median time to AIDS was estimated as 8.0 years in period 1 (CI: 6.0-10.6), 9.8 years in period 2 (CI: 8.5, 11.2), and 20.0 years in period 3 (CI: 17.1-23.3). This lengthening in time to AIDS from 1992 to 1999 was particularly marked in the period after the introduction of triple therapy, including protease inhibitors

From Black-Scholes and Dupire formulae to last passage times of local martingales. Part B : The finite time horizon

These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis

Biased Judges: Evidence from French Environmental Cases

Using an original database of 614 judgements in the French supreme courts from 1956 to 2010, we test for possible biases in judges’ decisions in the field of environmental accidents, focusing on a difference in treatment between private parties and the government as litigant. Two separate institutions deal with environmental cases in France, namely the Conseil d’Etat (Supreme Administrative Tribunal) for public utilities and central and local government, and the Cour de cassation (Supreme Civil Court) for private firms. We run bivariate Probit regressions to explain pro-defendant decisions and reversals of decisions. Overall, courts treat plaintiffs and defendants differently. A pro-defendant decision and a reversal of decision areless likely to occur: (i) when the appeal is initiated by the defendant rather than by the plaintiff; (ii) in the Conseil d’Etat ´ rather than in the Cour de cassation. The Conseil d’Etat ´ is harsher with defendants than the Cour de cassation. These results could be indicative of a bias of the lower administrative tribunals in favor of public utilities and/or the government

Short-time asymptotics for marginal distributions of semimartingales

We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior of call options with short maturity in a semimartingale model: whereas the behavior of \textit{out-of-the-money} options is found to be linear in time, the short time asymptotics of \textit{at-the-money} options is shown to depend on the fine structure of the semimartingale