Author

Frédéric Vrins

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Preprint Sep 2026

Exact calibration of structural models via time-change

In this note, we propose a general structural approach to model a default time $\tau$ as the first-passage time (FPT) of a (``firm-value'') process $S$ below a (``debt'') barrier $K$ that comply with a pre-specified survival probability curve $G(t)=\Pr(\tau>t)$. Following an idea of Mbaye and Vrins (Mathematical Financ...

F. Vrins, D. Brigo · 0 citations

Preprint Jul 2026

On the boundaries, asymptotic law and Bernoulli-Doob representation of homogeneous bounded martingales

We study homogeneous diffusion martingales evolving in a bounded state space $D=[a,b]$, where $a$ and $b$ are zeros of the diffusion coefficient. We call a process of the form $Z_t=\mathbb{E}[B\mid\mathcal{F}_t]$, with $B$ a Bernoulli random variable, a Bernoulli-Doob martingale. Our main results establish a complete e...

D. Brigo, Frédéric Vrins · 1 citation