Pricing Continuously Monitored Barrier Options under the SABR Model: A Closed-Form Approximation

Nian Yang, Yanchu Liu, Zhenyu Cui

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The stochastic alpha beta rho (SABR) model introduced by Hagan et al. (2002) is widely used in both fixed income and the foreign exchange (FX) markets. Continuously monitored barrier option contracts are among the most popular derivative contracts in the FX markets. In this paper, we develop closed-form formulas to approximate various types of barrier option prices (down-and-out/in, up-and-out/in) under the SABR model. We first derive an approximate formula for the survival density. The barrier option price is the one-dimensional integral of its payoff function and the survival density, which can be easily implemented and quickly evaluated. The approximation error of the survival density is also analyzed. To the best of our knowledge, it is the first time that analytical (approximate) formulas for the survival density and the barrier option prices for the SABR model are derived. Numerical experiments demonstrate the validity and efficiency of these formulas.

Original languageEnglish
Pages (from-to)116-131
Number of pages16
JournalJournal of Management Science and Engineering
Volume2
Issue number2
DOIs
StatePublished - Jun 2017

Keywords

  • Closed-form approximation
  • Continuously monitored barrier option
  • SABR model
  • Stochastic volatility
  • Survival density

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