Monte Carlo sampler of first-passage times for fractional Brownian motion using adaptive bisections: Source code

Benjamin Walter¹, Kay Jörg Wiese²
¹ Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.
² Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France.

Abstract

This C code is a Monte Carlo sampler to generate first-passage times of a fractional Brownian Motion fast and with high numerical accuracy. Let $X_t$ be a fractional Brownian Motion of Hurst parameter $H$, $\mu$ linear and $\nu$ fractional drift coefficients, then define $$ Z_t = X_t + \mu t + \nu t ^ { 2 H} $$ to be the fBM with drift, starting at $Z_0 = 0$. For given $m > 0$, this code finds the first time for which $Z_t \ge m$.

Source Code: [hal-02270046] [github]

The underlying algorithm is explained in arXiv:1908.11634

Code employed in arXiv:1908.10801 [abs] [pdf]