Pricing Path-Dependent Securities by the Extended Tree Method

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

Management Science, 2004, vol. 50, issue 9, 1235-1248

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.

Keywords: options; path-dependent securities; supplementary variable technique; CMO; average options (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:50:y:2004:i:9:p:1235-1248

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