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Affine Processes, Arbitrage-Free Term Structures Of Legendre Polynomials, And Option Pricing

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  • CAIO IBSEN RODRIGUES DE ALMEIDA

    ()
    (IBMEC Business School, Av. Rio Branco 108, 17th floor, 20040-001, Rio de Janeiro, RJ, Brazil)

Abstract

Multivariate Affine term structure models have been increasingly used for pricing derivatives in fixed income markets. In these models, uncertainty of the term structure is driven by a state vector, while the short rate is an affine function of this vector. The model is characterized by a specific form for the stochastic differential equation (SDE) for the evolution of the state vector. This SDE presents restrictions on its drift term which rule out arbitrages in the market. In this paper we solve the following inverse problem: Suppose the term structure of interest rates is modelled by a linear combination of Legendre polynomials with random coefficients. Is there any SDE for these coefficients which rules out arbitrages? This problem is of particular empirical interest because the Legendre model is an example of factor model with clear interpretation for each factor, in which regards movements of the term structure. Moreover, the Affine structure of the Legendre model implies knowledge of its conditional characteristic function. From the econometric perspective, we propose arbitrage-free Legendre models to describe the evolution of the term structure. From the pricing perspective, we follow Duffie et al. [22] in exploring their conditional characteristic functions to obtain a computational tractable method to price fixed income derivatives.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 08 (2005)
Issue (Month): 02 ()
Pages: 161-184

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Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:02:p:161-184

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Keywords: Consistent term structure models; Multifactor affine processes; Legendre polynomials; derivatives pricing;

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Cited by:
  1. Varga, Gyorgy, 2009. "Teste de Modelos Estatísticos para a Estrutura a Termo no Brasil
    [Test of Term Structure Models for Brazil]
    ," MPRA Paper 20832, University Library of Munich, Germany.
  2. Almeida, Caio Ibsen Rodrigues de & Vicente, José Valentim M., 2007. "The Role of No-Arbitrage on Forecasting: Lessons from a Parametric Term Structure Model," Economics Working Papers (Ensaios Economicos da EPGE) 657, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).

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