A binomial approximation for two-state Markovian HJM models |
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Authors: | Massimo Costabile Ivar Massabó Emilio Russo |
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Institution: | 1.Department of Business Administration,University of Calabria,Rende,Italy |
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Abstract: | 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. |
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