Bond valuation for generalized Langevin processes with integrated Lévy noise

Alex Paseka and Aerambamoorthy Thavaneswaran

Journal of Risk Finance, 2017, vol. 18, issue 5, 541-563

Abstract: Purpose - Recently,Steinet al.(2016)studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process ofSteinet al.(2016). Design/methodology/approach - Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise. Findings - The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases. Originality/value - Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.

Keywords: Default-free zero-coupon bond valuation; Generalized Langevin process; Lévy processes (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eme:jrfpps:jrf-09-2016-0125

DOI: 10.1108/JRF-09-2016-0125

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