Asia-Pacific Financial Markets

, Volume 19, Issue 3, pp 205–232

Pricing Discrete Barrier Options Under Stochastic Volatility

  • Kenichiro Shiraya
  • Akihiko Takahashi
  • Toshihiro Yamada

DOI: 10.1007/s10690-011-9147-3

Cite this article as:
Shiraya, K., Takahashi, A. & Yamada, T. Asia-Pac Financ Markets (2012) 19: 205. doi:10.1007/s10690-011-9147-3


This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in pricing barrier options with discrete monitoring. To the best of our knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Furthermore, it provides numerical examples for pricing double barrier call options with discrete monitoring under Heston and λ-SABR models.


Discrete barrier option Barrier option Knock-out option Double barrier option Stochastic volatility CEV model Heston model SABR model λ-SABR model Asymptotic expansion Malliavin calculus 

Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Kenichiro Shiraya
    • 1
    • 2
  • Akihiko Takahashi
    • 1
  • Toshihiro Yamada
    • 3
  1. 1.Graduate School of EconomicsThe University of TokyoTokyoJapan
  2. 2.Mizuho-DL Financial Technology Co., Ltd.TokyoJapan
  3. 3.Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. (MTEC)TokyoJapan

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