Barrier option pricing by branching processes

Georgi K. Mitov, Svetlozar T. Rachev, Young Shin Kim, Frank J. Fabozzi

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.

Original languageEnglish
Pages (from-to)1055-1073
Number of pages19
JournalInternational Journal of Theoretical and Applied Finance
Issue number7
StatePublished - Nov 2009


  • Barrier option
  • Bienayme-Galton-Watson branching process
  • Branching process in a random environment
  • Up-and-out call option


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