Approximating Risk Premium on a Parametric Arbitrage-Free Term Structure Model

45 Pages Posted: 10 Dec 2014 Last revised: 15 Apr 2015

See all articles by Caio Almeida

Caio Almeida

Getulio Vargas Foundation ; Princeton University

Kym Ardison

Getulio Vargas Foundation (FGV) - FGV/EPGE Escola Brasileira de Economia e Finanças

Daniela Kubudi

Getulio Vargas Foundation (FGV) - FGV/EPGE Escola Brasileira de Economia e Finanças

Date Written: April 14, 2015

Abstract

In this paper we approximate the risk factors of a polynomial arbitrage-free dynamic term structure model by running a sequential set of linear regressions independent across time. This approximation avoids the cost of a full optimization procedure allowing for a simple method to extract the risk premium embedded in interest rate assets. Closed-form bond pricing formulas provide interpretation of each source of aggregate risk as known term structure movements. Assuming, for illustrative purposes, an economy with three sources of aggregate risk (level, slope and curvature), we test the validity of our approximation adopting a dataset of Brazilian zero coupon interest rates. The new methodology generates accurate parameters, standard deviations and risk premium dynamics when compared to the exact dynamic model. Moreover, an empirical illustration comparing the out-of-sample forecasting performance of the exact model, our approximation, and a standard Gaussian affine model against the Random Walk, reveals that the proposed approximation obtains favorable forecasting results providing a reliable substitute to the exact estimation method with a much smaller computational time.

Keywords: Term structure of interest rates, parametric models, affine models, cross sectional estimation, time series analysis, forecasting

JEL Classification: C1, C5, G1

Suggested Citation

Almeida, Caio and Ardison, Kym and Kubudi, Daniela, Approximating Risk Premium on a Parametric Arbitrage-Free Term Structure Model (April 14, 2015). Available at SSRN: https://ssrn.com/abstract=2535766 or http://dx.doi.org/10.2139/ssrn.2535766

Caio Almeida (Contact Author)

Getulio Vargas Foundation ( email )

Praia de Botafogo 190, 11o andar
Botafogo
Rio de Janeiro, Rio de Janeiro 22250-900
Brazil
5521-37995827 (Phone)
5521-2553-8821 (Fax)

HOME PAGE: http://www.fgv.br/professor/calmeida/

Princeton University ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States

Kym Ardison

Getulio Vargas Foundation (FGV) - FGV/EPGE Escola Brasileira de Economia e Finanças ( email )

Praia de Botafogo 190/1125, CEP
Rio de Janeiro RJ 22253-900
Brazil

Daniela Kubudi

Getulio Vargas Foundation (FGV) - FGV/EPGE Escola Brasileira de Economia e Finanças ( email )

Praia de Botafogo 190/1125, CEP
Rio de Janeiro RJ 22253-900
Brazil

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