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Efficient willow tree method for European-style and American-style moving average barrier options pricing

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  • Ling Lu
  • Wei Xu
  • Zhehui Qian

Abstract

Moving average options are widely traded in financial markets, but exiting methods for pricing this type of option are too slow. This paper proposes two efficient willow tree methods for pricing European-style and American-style moving average barrier options (MABOs). We first solve the finite-dimensional partial differential equation model for discretely monitored MABOs by willow tree methods, and then compute the value of continuously monitored MABOs by Richardson’s two-point extrapolation. Our new willow tree method employs the interpolation error minimization technique to reduce complexity. The corresponding convergence rate and error bounds are also analyzed. It shows that our proposed methods can provide the same accuracy as the binomial tree approach and Monte Carlo simulation, but require much less computing time. The numerical experiments support our claims.

Suggested Citation

  • Ling Lu & Wei Xu & Zhehui Qian, 2017. "Efficient willow tree method for European-style and American-style moving average barrier options pricing," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 889-906, June.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:6:p:889-906
    DOI: 10.1080/14697688.2016.1231416
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