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Optimal exercise frontier of Bermudan options by simulation methods

Author

Listed:
  • Dejun Xie

    (Financial and Actuarial Mathematics, Xi’an Jiaotong Liverpool University, Suzhou, China)

  • David A. Edwards

    (��Mathematical Sciences, University of Delaware, Newark, DE 19716, USA)

  • Xiaoxia Wu

    (��Department of Mathematics, The University of Texas at Austin, Austin, USA)

Abstract

In this paper, a novel algorithm for determining the free exercise boundary for high-dimensional Bermudan option problems is presented. First, a rough estimate of the boundary is constructed on a fine (daily) time grid. This rough estimate is used to generate a more accurate estimate on a coarse time grid (exercise opportunities). Antithetic branching is used to reduce the computational workload. The method is validated by comparing it with other methods of solving the standard Black–Scholes problem. Finally, the method is applied to two cases of Bermudan options with a second stochastic variable: a stochastic interest rate and a stochastic volatility.

Suggested Citation

  • Dejun Xie & David A. Edwards & Xiaoxia Wu, 2022. "Optimal exercise frontier of Bermudan options by simulation methods," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 1-20, September.
    • Handle: RePEc:wsi:ijfexx:v:09:y:2022:i:03:n:s242478632250013x
    DOI: 10.1142/S242478632250013X
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