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Term structure modelling for multiple curves with stochastic discontinuities

Claudio Fontana (), Zorana Grbac (), Sandrine Gümbel () and Thorsten Schmidt ()
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Claudio Fontana: University of Padova
Zorana Grbac: Université Paris Diderot
Sandrine Gümbel: University of Freiburg
Thorsten Schmidt: University of Freiburg

Finance and Stochastics, 2020, vol. 24, issue 2, No 7, 465-511

Abstract: Abstract We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework and provide a fundamental theorem of asset pricing based on NAFLVR. The approach with stochastic discontinuities permits to embed market models directly, unifying seemingly different modelling philosophies. We also develop a tractable class of models, based on affine semimartingales, going beyond the requirement of stochastic continuity.

Keywords: HJM model; Semimartingale; Affine process; NAFLVR; Large financial market; 60G44; 60G48; 60G57; 91B70; 91G20; 91G30 (search for similar items in EconPapers)
JEL-codes: C02 C60 E43 G12 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00780-020-00416-5

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