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Pricing And Deltas Of Discretely-Monitored Barrier Options Using Stratified Sampling On The Hitting-Times To The Barrier

Author

Listed:
  • MARK JOSHI

    (Centre for Actuarial Studies, University of Melbourne, Victoria, VIC3010, Australia)

  • ROBERT TANG

    (Centre for Actuarial Studies, University of Melbourne, Victoria, VIC3010, Australia)

Abstract

We develop new Monte Carlo techniques based on stratifying the stock's hitting-times to the barrier for the pricing and Delta calculations of discretely-monitored barrier options using the Black-Scholes model. We include a new algorithm for sampling an Inverse Gaussian random variable such that the sampling is restricted to a subset of the sample space. We compare our new methods to existing Monte Carlo methods and find that they can substantially improve convergence speeds.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:05:n:s0219024910005978
    DOI: 10.1142/S0219024910005978
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    Citations

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    Cited by:

    1. 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.
    2. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.

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