Pricing Double Barrier Options by Combinatorial Approaches

  • Tian-Shyr Dai
  • Yuh-Dauh Lyuu
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 29)


Double barrier options are important path-dependent derivatives in the financial market. How to price them efficiently and accurately is thus important. Until now, no simple closed-form pricing formula for double barrier options is reported. Double barrier options can be priced on a lattice that divides a certain time interval (from option initial date to maturity date) into n equal-length time steps. The pricing results obtained by the lattice algorithm converge to the true option value as n → ∞, and the results oscillate significantly especially when n is not large enough. To obtain an accurate pricing result without suffering from price oscillation, n is required to be a large number. Unfortunately, the lattice pricing algorithm runs in O(n 2) time. This paper proposes a linear-time combinatorial algorithm that can generate the same pricing results as the lattice algorithm. Thus our algorithm can handle very large n’s efficiently. This algorithm uses a novel technique based on the reflection principle and the inclusion-exclusion principle. Numerical experiments are given to verify the excellent performance of our algorithm.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bhagavatula RS, and Carr PP (1997) Valuing Double Barrier Options with Fourier Series. Manuscript, New York University, NY, USA.Google Scholar
  2. 2.
    Cox J, Ross S, Rubinstein M (1979) Option Pricing: A Simplified Approach. J. Financial Econom. 7:229–264.CrossRefMATHGoogle Scholar
  3. 3.
    Figlewski S, Gao B (1999) The Adaptive Mesh Model: A New Approach to Efficient Option Pricing. J. Financial Econom. 53:313–351.CrossRefGoogle Scholar
  4. 4.
    Geman H, and Yor M (1996) Pricing and Hedging Double-Barrier Options: A Probabilistic Approach. Math. Finance 6:365–378.MATHCrossRefGoogle Scholar
  5. 5.
    Lyuu YD (1998) Very Fast Algorithms for Barrier Option Pricing and the Ballot Problem. J. Derivatives 5:68–79.Google Scholar
  6. 6.
    Ritchken P (1995) On Pricing Barrier Options. J. Derivatives 3:19–28.Google Scholar
  7. 7.
    Wei, JZ (1998) Valuation of Discrete Barrier Options by Interpolations. J. Derivatives, 6:51–73.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Applied MathematicsChung-Yuan Christian UniversityTao-Yuan countyTaiwan
  2. 2.Department of Finance and Department of Computer Science & Information EngineeringNational Taiwan UniversityTaipeiTaiwan

Personalised recommendations