Short maturity asian options in local volatility models

Dan Pirjol, Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We present a rigorous study of the short maturity asymptotics for Asian options with continuous- time averaging, under the assumption that the underlying asset follows a local volatility model. The asymptotics for out-of-the-money, in-the-money, and at-the-money cases are derived, considering both fixed strike and oating strike Asian options. The asymptotics for the out-of-the-money case involve a nontrivial variational problem which is solved completely. We present an analytical ap- proximation for Asian options prices and demonstrate good numerical agreement of the asymptotic results with the results of Monte Carlo simulations and benchmark test cases in the Black{Scholes model for option parameters relevant in practical applications.

Original languageEnglish
Pages (from-to)947-992
Number of pages46
JournalSIAM Journal on Financial Mathematics
Volume7
Issue number1
DOIs
StatePublished - 2016

Keywords

  • Asian options
  • Large deviations
  • Local volatility
  • Short maturity
  • Variational problem

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