Multi-Lag Term Structure Models with Stochastic Risk Premia

Alain Monfort and Fulvio Pegoraro ()

Working papers from Banque de France

Abstract: The purpose of this paper is to propose discrete-time term structure models where the historical dynamics of the factor (xt) is given, in the univariate case, by a Gaussian AR(p) process, and, in the multivariate case, by a Gaussian n-dimensional VAR(p) process. The factor (xt) is considered as a latent or an observable variable and, in the second case, (xt) is given by the short rate (in the scalar setting) or by a vector of several yields (in the multivariate setting). We consider an exponential-affine stochastic discount factor (SDF) with a stochastic factor risk correction coefficient defined, at time t, as an affine function of Xt = (xt, . . . , xt?p+1)0 and, consequently, the yield-to-maturity formula at time t is an affine function of the p most recent lagged values of xt+1. We study the Gaussian AR(p) and the Gaussian VAR(p) Factor-Based Term Structure Models. We investigate, under the risk-neutral and the S-forward probability, the Moving Average (or discrete-time Heath, Jarrow and Morton) representation of the yield and short-term forward rate processes. This representation gives the possibility to exactly replicate the currently-observed yield curve. We also study the problem of matching the theoretical and currently-observed market term structure by means of the Extended AR(p) approach.

Keywords: Discrete-time Affine Term Structure Models; Stochastic Discount Factor, Gaussian VAR(p) processes; Stochastic risk premia; Moving Average or discrete-time HJM representations; Exact Fitting of the currently-observed yield curve. (search for similar items in EconPapers)
JEL-codes: C1 C5 G1 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Working Paper: Multi-Lag Term Structure Models with Stochastic Risk Premia (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:bfr:banfra:189

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