Asymptotics for the discrete-Time average of the geometric Brownian motion and Asian options

Dan Pirjol, Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-Time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps. We derive almost sure limit, fluctuations, large deviations, and also the asymptotics of the moment generating function of the average. Based on these results, we derive the asymptotics for the price of Asian options with discrete-Time averaging in the Black-Scholes model, with both fixed and floating strike.

Original languageEnglish
Pages (from-to)446-480
Number of pages35
JournalAdvances in Applied Probability
Volume49
Issue number2
DOIs
StatePublished - 1 Jun 2017

Keywords

  • Asian option
  • Berry-Esseen bound
  • central limit theorem
  • large deviations

Fingerprint

Dive into the research topics of 'Asymptotics for the discrete-Time average of the geometric Brownian motion and Asian options'. Together they form a unique fingerprint.

Cite this