Abstract

We demonstrate how to adjust the Katolay, Williams, and Fabozzi (1993) binomial tree model for pricing option-embedded bonds to have separate binomial trees for the forward rate process and for the component bond prices (actual bond prices or derived from a yield curve).  This reduces computational complexity at a given node within a single binomial tree.  Further, the calibration method is performed on “spine” values for the forward rate binomial tree, which is more consistent with the actual forward rates that are utilized as initial values in the calibration process.  The entire model is produced in Excel and uses new Excel functionality in the form of =LAMBDA functions.

KEY TAKEAWAYS:

We demonstrate how to adjust the Katolay, Williams, and Fabozzi (1993) binomial tree model for pricing option-embedded bonds to have separate binomial tress for the forward rate process and for the component bond prices.  This reduces computational complexity at a given node within a single binomial tree.

The forward rate binomial tree is based on “spine” values for the tree that are more consistent with the actual forward rates used to initialize the calibration of the tree to actual or yield curve implied bond prices.

The model is developed in Excel and uses new Excel functionality in the form of =LAMBDA functions.  This makes the model readily accessible and the =LAMBDA functions are not very complex for those unfamiliar with using the function.  If desired, the =LAMBDA functions can be copied to a new spreadsheet from a downloadable spreadsheet associated with this paper.

Document Type

Working Paper

Publication Date

2-19-2026

Publisher Statement

Please note that downloads of this working paper are for private/personal use only. Do not cite without permission.

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BOND-TREE.xlsx (38 kB)
BOND-TREE-CAL.xlsx (38 kB)

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