Term structure modeling under volatility uncertainty
Hölzermann J (2022)
Mathematics and Financial Economics 16(2): 317-343.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Abstract / Bemerkung
In this paper, we study term structure movements in the spirit of Heath et al. (Econometrica 60(1):77–105, 1992) under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift condition. In contrast to the traditional model, the drift condition consists of several equations and several market prices, termed market price of risk and market prices of uncertainty, respectively. The drift condition is still consistent with the classical one if there is no volatility uncertainty. Similar to the traditional model, the risk-neutral dynamics of the forward rate are completely determined by its diffusion term. The drift condition allows to construct arbitrage-free term structure models that are completely robust with respect to the volatility. In particular, we obtain robust versions of classical term structure models.
Stichworte
Term structure of interest rates;
No-arbitrage;
Ambiguous volatility;
Knightian uncertainty;
Model uncertainty;
Robust finance
Erscheinungsjahr
2022
Zeitschriftentitel
Mathematics and Financial Economics
Band
16
Ausgabe
2
Seite(n)
317 - 343
Urheberrecht / Lizenzen
ISSN
1862-9679
eISSN
1862-9660
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
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https://pub.uni-bielefeld.de/record/2958792
Zitieren
Hölzermann J. Term structure modeling under volatility uncertainty. Mathematics and Financial Economics. 2022;16(2):317-343.
Hölzermann, J. (2022). Term structure modeling under volatility uncertainty. Mathematics and Financial Economics, 16(2), 317-343. https://doi.org/10.1007/s11579-021-00310-4
Hölzermann, Julian. 2022. “Term structure modeling under volatility uncertainty”. Mathematics and Financial Economics 16 (2): 317-343.
Hölzermann, J. (2022). Term structure modeling under volatility uncertainty. Mathematics and Financial Economics 16, 317-343.
Hölzermann, J., 2022. Term structure modeling under volatility uncertainty. Mathematics and Financial Economics, 16(2), p 317-343.
J. Hölzermann, “Term structure modeling under volatility uncertainty”, Mathematics and Financial Economics, vol. 16, 2022, pp. 317-343.
Hölzermann, J.: Term structure modeling under volatility uncertainty. Mathematics and Financial Economics. 16, 317-343 (2022).
Hölzermann, Julian. “Term structure modeling under volatility uncertainty”. Mathematics and Financial Economics 16.2 (2022): 317-343.
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