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Finance and Stochastics

Erschienen in:

14.02.2020

Term structure modelling for multiple curves with stochastic discontinuities

verfasst von: Claudio Fontana, Zorana Grbac, Sandrine Gümbel, Thorsten Schmidt

Erschienen in: Finance and Stochastics | Ausgabe 2/2020

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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.

Vorheriger Artikel Trading strategies generated pathwise by functions of market weights

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Note that at the present level of generality, the rate \(r_{t}\) does not represent a riskless rate of return.

Note that we need to consider an extended set of maturities for OIS bonds since the payoff of an FRA contract with settlement date \(T\) and tenor \(\delta \) takes place at date \(T+\delta \).

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Titel: Term structure modelling for multiple curves with stochastic discontinuities
verfasst von: Claudio Fontana
Zorana Grbac
Sandrine Gümbel
Thorsten Schmidt
Publikationsdatum: 14.02.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Finance and Stochastics / Ausgabe 2/2020
Print ISSN: 0949-2984
Elektronische ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-020-00416-5

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