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Pricing Asian Options with an Efficient Convergent Approximation Algorithm

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

Summary

Asian options are popular path-dependent derivatives in the financial market. However, how to price them efficiently and accurately has been a longstanding research and practical problem. No known exact pricing formulas are available to price the Asian option. Although approximate pricing formulas exist, they lack accuracy guarantees. Asian options can be priced on the lattice. A lattice divides a time interval into n equal-length time steps. It is known that the value computed by the lattice converges to the true option value as n → ∞. Unfortunately, only subexponential-time algorithms are available if Asian options are to be priced on the lattice without approximations. Efficient approximation algorithms are available for the lattice. The best known in the literature is an O(n 3.5)-time approximation lattice algorithm and an O(n 3)-time approximation PDE algorithm. Our paper suggests an O(n 2.5)-time lattice algorithm. Our algorithm uses a novel technique based on the method of Lagrange multipliers to minimize the approximation error. Numerical results verify the accuracy and the excellent performance of our algorithm.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Tian-Shyr Dai
    • 1
  • Guan-Shieng Huang
    • 2
  • Yuh-Dauh Lyuu
    • 3
  1. 1.Department of Applied MathematicsChung-Yuan Christian UniversityTao-Yuan countyTaiwan
  2. 2.Department of Computer Science & Information EngineeringNational Chi Nan UniversityTaipeiTaiwan
  3. 3.Department of Finance and Department of Computer Science & Information EngineeringNational Taiwan UniversityTaipeiTaiwan

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