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

Claudio Fontana, Simone Pavarana and Wolfgang J. Runggaldier

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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 & Runggaldier (2013) 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 optimization problem of a representative investor.

Date: 2023-04, Revised 2023-10
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Published in Finance and Stochastics (2023), 27: 903-932

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