Review of Derivatives Research

, Volume 14, Issue 1, pp 37–65 | Cite as

A binomial approximation for two-state Markovian HJM models



This article develops a lattice algorithm for pricing interest rate derivatives under the Heath et al. (Econometrica 60:77–105, 1992) paradigm when the volatility structure of forward rates obeys the Ritchken and Sankarasubramanian (Math Financ 5:55–72) condition. In such a framework, the entire term structure of the interest rate may be represented using a two-dimensional Markov process, where one state variable is the spot rate and the other is an accrued variance statistic. Unlike in the usual approach based on the Nelson-Ramaswamy (Rev Financ Stud 3:393–430) transformation, we directly discretize the heteroskedastic spot rate process by a recombining binomial tree. Further, we reduce the computational cost of the pricing problem by associating with each node of the lattice a fixed number of accrued variance values computed on a subset of paths reaching that node. A backward induction scheme coupled with linear interpolation is used to evaluate interest rate contingent claims.


Interest rate options Contingent claims Binomial algorithms Discrete-time models 

JEL Classification

C63 G12 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Massimo Costabile
    • 1
  • Ivar Massabó
    • 1
  • Emilio Russo
    • 1
  1. 1.Department of Business AdministrationUniversity of CalabriaRendeItaly

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