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Conditional sampling for barrier option pricing under the LT method

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  • Nico Achtsis
  • Ronald Cools
  • Dirk Nuyens

Abstract

We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance reduction is achieved. We extend the method to allow pricing knock-in barrier options and introduce a root-finding method to obtain a further variance reduction. The effectiveness of the new method is supported by numerical results.

Suggested Citation

  • Nico Achtsis & Ronald Cools & Dirk Nuyens, 2011. "Conditional sampling for barrier option pricing under the LT method," Papers 1111.4808, arXiv.org, revised Dec 2012.
    • Handle: RePEc:arx:papers:1111.4808
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    References listed on IDEAS

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    1. Paul Glasserman & Jeremy Staum, 2001. "Conditioning on One-Step Survival for Barrier Option Simulations," Operations Research, INFORMS, vol. 49(6), pages 923-937, December.
    2. Pierre L'Ecuyer & Christiane Lemieux, 2000. "Variance Reduction via Lattice Rules," Management Science, INFORMS, vol. 46(9), pages 1214-1235, September.
    3. Mark Joshi & Robert Tang, 2010. "Pricing And Deltas Of Discretely-Monitored Barrier Options Using Stratified Sampling On The Hitting-Times To The Barrier," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 717-750.
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