A stochastic control perspective on term structure models with roll-over risk

Claudio Fontana (), Simone Pavarana () and Wolfgang J. Runggaldier ()
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Claudio Fontana: University of Padova
Simone Pavarana: University of Freiburg
Wolfgang J. Runggaldier: University of Padova

Finance and Stochastics, 2023, vol. 27, issue 4, No 4, 903-932

Abstract: Abstract In this paper, we consider a generic interest rate market in the presence of roll-over risk, which generates spreads in spot/forward term rates. We do not require classical absence of arbitrage and rely instead on a minimal market viability assumption, which enables us to work in the context of the benchmark approach. In a Markovian setting, we extend the control-theoretic approach of Gombani and Runggaldier (Math. Finance 23 (2013) 659–686) and derive representations of spot/forward spreads as value functions of suitable stochastic optimal control problems, formulated under the real-world probability and with power-type objective functionals. We determine endogenously the funding–liquidity spread by relating it to the risk-sensitive optimisation problem of a representative investor.

Keywords: Roll-over risk; Liquidity risk; Interest rate; Multiplicative spread; Term rate; Benchmark approach; Stochastic control; Risk-sensitive portfolio optimisation; 60G44; 91G30; 93E20 (search for similar items in EconPapers)
JEL-codes: C02 C61 E43 G12 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00780-023-00515-z

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