Term-Structure Models Using Binomial Trees* Publisher: The Research Foundation of AIMR (CFA Institute)

Number Of Pages: 104
Publication Date: 2001-11-15
ISBN: 9780943205533





Term-structure models are essential for the valuation of interest rate dependent claims. Although term-structure experts have produced a variety of useful models, they involve complex mathematics, which limits their accessibility to investment practitioners who are not engaged in this area of specialization. Moreover, the original “journal” versions of these models and their subsequent descriptions in text books often abstract from many important details necessary for implementation. These circumstances makeit difficult for investors to compare the prices of interest rate dependent claims, to assess the appropriateness of alternativeterm-structure software products, and to build their own term-structure models. With this monograph, Gerald W. Buetow, Jr., CFA, and James Sochacki go a long way toward ameliorating this problem. They begin with a concise but hardly superficial overview of interest rate modeling, and they introduce the binomial tree framework. Having thoroughly prepared the reader, they next present the five most important no-arbitrage term-structure models: • Ho–Lee Model. This model was the first no-arbitrage term-structure model. It assumes constant and identical volatility for all spot and forward rates and does not incorporate mean reversion.• Hull–White Model. This model extends the Ho–Lee model to allow for mean reversion.• Kalotay–Williams–Fabozzi Model. This model assumes a lognormal distribution and eliminates the problem of negative short rates, which can occur with the Ho–Lee and Hull–White models.• Black–Karasinski Model. An extension of the Kalotay–Williams–Fabozzi Model, this model controls the growth in the short rate.• Black–Derman–Toy Model. This model permits independent and timevarying spot-rate volatilities.