### Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion

Hölzermann J, Lin Q (2019) Center for Mathematical Economics Working Papers; 613.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch

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Abstract / Bemerkung
We show how to set up a forward rate model in the presence of volatility uncertainty by using the theory of G-Brownian motion. In order to formulate the model, we extend the G-framework to integration with respect to two integrators and prove a version of Fubini's theorem for stochastic integrals. The evolution of the forward rate in the model is described by a diffusion process, which is driven by a G-Brownian motion. 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 two equations and two market prices of risk, respectively, uncertainty. Furthermore, we examine the connection to short rate models and discuss some examples.
Stichworte
Robust Finance; Knightian Uncertainty; Interest Rates; No-Arbitrage
Erscheinungsjahr
2019
Serientitel
Center for Mathematical Economics Working Papers
Band
613
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2934840

### Zitieren

Hölzermann J, Lin Q. Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion . Center for Mathematical Economics Working Papers. Vol 613. Bielefeld: Center for Mathematical Economics; 2019.
Hölzermann, J., & Lin, Q. (2019). Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion (Center for Mathematical Economics Working Papers, 613). Bielefeld: Center for Mathematical Economics.
Hölzermann, J., and Lin, Q. (2019). Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion . Center for Mathematical Economics Working Papers, 613, Bielefeld: Center for Mathematical Economics.
Hölzermann, J., & Lin, Q., 2019. Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion , Center for Mathematical Economics Working Papers, no.613, Bielefeld: Center for Mathematical Economics.
J. Hölzermann and Q. Lin, Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion , Center for Mathematical Economics Working Papers, vol. 613, Bielefeld: Center for Mathematical Economics, 2019.
Hölzermann, J., Lin, Q.: Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion . Center for Mathematical Economics Working Papers, 613. Center for Mathematical Economics, Bielefeld (2019).
Hölzermann, Julian, and Lin, Qian. Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion . Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 613.
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