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Pricing Path-Dependent Securities by the Extended Tree Method

Author

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  • Naoki Kishimoto

    (Faculty of Business Administration, Hosei University, 2-17-1 Fujimi, Chiyoda-ku, Tokyo 102-8160, Japan)

Abstract

This paper presents a discrete-time method (ET method) for pricing path-dependent securities by the supplementary variable technique and examines the ET method from the point of view of Arrow-Debreu event tree. In particular, this paper identifies sufficient conditions on supplementary variables under which the ET method yields the same price for a path-dependent security as a valuation method based on a comparable Arrow-Debreu event tree. Two examples are provided to illustrate the ET method. The first example is a valuation of collateralized mortgage obligations (CMOs), where the collateral of a CMO is modeled as a pool of mortgage loans with heterogeneous prepayment costs. The second example is a valuation of American average options where the average is computed over a moving period with a fixed length. In addition, this paper presents a measure for the computational size of the ET method and illustrates numerical advantages of the ET method with examples.

Suggested Citation

  • Naoki Kishimoto, 2004. "Pricing Path-Dependent Securities by the Extended Tree Method," Management Science, INFORMS, vol. 50(9), pages 1235-1248, September.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:9:p:1235-1248
    DOI: 10.1287/mnsc.1030.0198
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    References listed on IDEAS

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    Cited by:

    1. Wei Xu & Zhiwu Hong & Chenxiang Qin, 2013. "A new sampling strategy willow tree method with application to path-dependent option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 861-872, May.

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