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

TL;DR

This paper models interest rate markets with roll-over risk using a stochastic control framework, deriving spreads as optimal control problems without requiring classical no-arbitrage conditions.

Contribution

It extends the control theoretic approach to include roll-over risk in a market viability setting, providing a novel representation of spreads as solutions to stochastic control problems.

Findings

Derives explicit formulas for spot and forward spreads.

Links funding-liquidity spread to risk-sensitive optimization.

Operates under minimal market viability assumptions.

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.