A regime switching model to evaluate bonds in a quadratic term structure of interest rates

Stéphane Goutte (1, 2) , Raphaël Homayoun (3, 2) , Thomas Porcher (2)

1 BF - Banque-Finance
2 ESG Research Lab
3 City University London

In this article, we consider a discrete time economy in which we assume that the short term interest rate follows a quadratic term structure in a regime switching asset process. The possible non-linear structure and the fact that the interest rate can have different economic or financial trends justify Regime Switching Quadratic Term Structure Model (RS-QTSM). Indeed, this regime switching process depends on the values of a Markov chain with a time dependent transition probability matrix which can capture the different states (regimes) of the economy. We prove that under this model, the conditional zero coupon bond price admits a quadratic term structure. Moreover, the stochastic coefficients which appear in this decomposition satisfy an explicit system of coupled stochastic backward recursions.

Mots clés: Regime switching; Quadratic term structure model; Zero coupon bond; Markov chain

Domaines: Economies et finances; Mathématiques [math]; Applications [stat.AP]; Probabilités [math.PR]; Statistiques [math.ST]; Économie et finance quantitative [q-fin]; Finance quantitative [q-fin.CP]; Pricing [q-fin.PR]; Econométrie de la finance [q-fin.ST]

Stéphane Goutte, Raphaël Homayoun, Thomas Porcher. A regime switching model to evaluate bonds in a quadratic term structure of interest rates. 2014. ⟨hal-01090846⟩