Markovian short rates in multidimensional term structure Lévy models

Volume 122 / 2020

Pavel V. Gapeev, Uwe Küchler Banach Center Publications 122 (2020), 93-106 MSC: Primary 60J60, 60J75, 91B70; Secondary 60J25, 60H10, 60G51. DOI: 10.4064/bc122-6

Abstract

We study a bond market model and the related term structure of interest rates in which the prices of zero coupon bonds are driven by a multidimensional Lévy process. We show that the short rate forms a Markov process if and only if the deterministic forward rate volatility coefficients are decomposed into products of two factors where the factor depending on the maturity time is the same for all components. The proof is based on the analysis of sample path properties of the underlying multidimensional process.

Authors

  • Pavel V. GapeevLondon School of Economics
    Department of Mathematics
    Houghton Street
    London WC2A 2AE, United Kingdom
    e-mail
  • Uwe KüchlerHumboldt University of Berlin
    Institute of Mathematics
    Unter den Linden 6
    D-10099 Berlin, Germany
    e-mail

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