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A State‐Space Partitioning Method For Pricing High‐Dimensional American‐Style Options

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  • Xing Jin
  • Hwee Huat Tan
  • Junhua Sun

Abstract

The pricing of American‐style options by simulation‐based methods is an important but difficult task primarily due to the feature of early exercise, particularly for high‐dimensional derivatives. In this paper, a bundling method based on quasi‐Monte Carlo sequences is proposed to price high‐dimensional American‐style options. The proposed method substantially extends Tilley's bundling algorithm to higher‐dimensional situations. By using low‐discrepancy points, this approach partitions the state space and forms bundles. A dynamic programming algorithm is then applied to the bundles to estimate the continuation value of an American‐style option. A convergence proof of the algorithm is provided. A variety of examples with up to 15 dimensions are investigated numerically and the algorithm is able to produce computationally efficient results with good accuracy.

Suggested Citation

  • Xing Jin & Hwee Huat Tan & Junhua Sun, 2007. "A State‐Space Partitioning Method For Pricing High‐Dimensional American‐Style Options," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 399-426, July.
    • Handle: RePEc:bla:mathfi:v:17:y:2007:i:3:p:399-426
    DOI: 10.1111/j.1467-9965.2007.00309.x
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    Cited by:

    1. Adam W. Kolkiewicz & Fangyuan Sally Lin, 2017. "Pricing Surrender Risk in Ratchet Equity-Index Annuities under Regime-Switching Lévy Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 433-457, July.
    2. Patrik Karlsson & Shashi Jain & Cornelis W. Oosterlee, 2016. "Fast and accurate exercise policies for Bermudan swaptions in the LIBOR market model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-22, March.
    3. Wei, Wei & Zhu, Dan, 2022. "Generic improvements to least squares monte carlo methods with applications to optimal stopping problems," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1132-1144.
    4. Jin, Xing & Yang, Cheng-Yu, 2016. "Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 65-77.
    5. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.

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