On the distribution of the time-integral of the geometric Brownian motion

Péter Nándori, Dan Pirjol

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study the numerical evaluation of several functions appearing in the small time expansion of the distribution of the time-integral of the geometric Brownian motion as well as its joint distribution with the terminal value of the underlying Brownian motion. A precise evaluation of these distributions is relevant for the simulation of stochastic volatility models with log-normally distributed volatility, and Asian option pricing in the Black–Scholes model. We derive series expansions for these distributions, which can be used for numerical evaluations. Using tools from complex analysis, we determine the convergence radius and large order asymptotics of the coefficients in these expansions. We construct an efficient numerical approximation of the joint distribution of the time-integral of the gBM and its terminal value, and illustrate its application to Asian option pricing in the Black–Scholes model.

Original languageEnglish
Article number113818
JournalJournal of Computational and Applied Mathematics
Volume402
DOIs
StatePublished - 1 Mar 2022

Keywords

  • Asymptotic expansions
  • Complex analysis
  • Numerical approximation

Fingerprint

Dive into the research topics of 'On the distribution of the time-integral of the geometric Brownian motion'. Together they form a unique fingerprint.

Cite this