A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models

Authors: Kramin, Marat¹; Kramin, Timur²; Young, Stephen³; Dharan, Venkat⁴

Source: Review of Quantitative Finance and Accounting, Volume 24, Number 2, March 2005 , pp. 199-226(28)

Publisher: Springer

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Abstract:

This paper presents an alternative approach for interest rate lattice construction in the Ritchken and Sankarasubramanian (1995) framework. The proposed method applies a parsimonious induction technique to represent the distribution of auxiliary state variables and value interest rate derivatives. In contrast to other approaches, this technique requires no numerical interpolations, approximations and iterative procedures for pricing interest rate options using a simple backward induction and, therefore, provides significant computational advantages and flexibility with respect to existing implementations. Also, the proposed trinomial interest rate lattice specification provides for a further reduction in computational costs with additional flexibility. The results of this work can be extended to a class of derivatives pricing models with path dependent state variables and generalized to multi-factor models.

Keywords: induction; multi-state-variable Markov process; trinomial lattice; derivatives valuation

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11156-005-6337-y

Affiliations: 1: Fannie Mae Portfolio Strategy Department, 2500 Wisconsin Avenue, NW, Apt. #141, Washington DC, 20007, Email: marat_kramin@fanniemae.com 2: MTS, Kazan, Russia, 3: Wachovia CIB Risk Management, USA, 4: Fannie Mae Portfolio Strategy Department, USA,

Publication date: 2005-03-01