A time-varying Markov chain model of term structure.
type: Item
instance of: scholarly article
title: A time-varying Markov chain model of term structure.
zbMATH Open document ID: 1037.60070
DOI: 10.1016/S0167-7152(02)00313-9
author: Rogemar Mamon
published in: Statistics \& Probability Letters
publication date: 2003-05-07T00:00:00Z
review text: Term structure is a widespread financial terminology refering to the length of investment, for instance trying to explain the differences between short-term, medium-term and long-term nominal interest rates. In this time-varying Markov chain model, the instantaneous interest rate at time \(s\) is a function \(r(s,X_s)\), where \(X\) is a continuous time Markov chain on a finite state space with time-dependent transition rates: \[ \frac{d}{dt}P(X_t=i)=\sum_j a_{ij} P(X_t=j). \] The paper gives a computation of \(E(\exp(-\int_t^T r(s,X_s)\,ds))\) through differential systems. It amounts to the following. Denote \[ \varphi_i(t,T)= E\left(1_{X_T=i} \exp\Biggl(-\int_t^T r(s,X_s)\,ds \Biggr) \right), \] which is \(E(\langle V(t,T),e_i\rangle)\) in the notations of the paper. Then \[ \frac{d}{dT}\varphi_i(t,T) =\sum_j a_{ij}(T) \varphi_j(t,T) -r(T,i) \varphi_i(t,T). \]
reviewed by: Thierry Delmotte
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 91B28
zbMATH DE Number: 1907006
zbMATH Keywords: Markov chain
zbMATH Keywords: term structure
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1907006