Generalizations of Ho–Lee’s binomial interest rate model I: from one- to multi-factor |
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| Authors: | Jirô Akahori Hiroki Aoki Yoshihiko Nagata |
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| Institution: | (1) Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu Shiga, 525-8577, Japan;(2) Department of Mathematics, Tokyo University of Science, Noda Chiba, 278-8510, Japan;(3) Risk Management Department, Mizuho Trust & Banking Co. Ltd., 1-2-1 Yaesu, Tokyo 103-8670, Japan |
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| Abstract: | In this paper a multi-factor generalization of Ho–Lee model is proposed. In sharp contrast to the classical Ho–Lee, this generalization
allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is a process
with stationary independent increments to be compatible with principal component analysis. Based on the model, generalizations
of duration-based hedging are proposed. A continuous-time limit of the model is also discussed.
This research was supported by Open Research Center Project for Private Universities: matching fund subsidy from MEXT, 2004–2008
and also by Grants-in-Aids for Scientific Research (No. 18540146) from the Japan Society for Promotion of Sciences. |
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| Keywords: | Ho– Lee model Duration Multi-factor Recombining tree Stationary increments Forward rate Drift condition |
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