A Consistent Stochastic Model of the Term Structure of Interest Rates for Multiple Tenors

52 Pages Posted: 25 May 2017 Last revised: 17 Sep 2018

See all articles by Mesias Alfeus

Mesias Alfeus

Department of Statistics and Actuarial Science - Stellenbosch University

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Erik Schlögl

University of Technology Sydney (UTS), Quantitative Finance Research Centre; University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management; Faculty of Science, Department of Statistics, University of Johannesburg; Financial Research Network (FIRN)

Date Written: May 22, 2017

Abstract

Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor ("roll-over risk"), we construct a stochastic model framework for the term structure of interest rates in which a frequency basis (i.e. a spread applied to one leg of a swap to exchange one floating interest rate for another of a different tenor in the same currency) arises endogenously. This roll-over risk consists of two components, a credit risk component due to the possibility of being downgraded and thus facing a higher credit spread when attempting to roll over short-term borrowing, and a component reflecting the (systemic) possibility of being unable to roll over short-term borrowing at the reference rate (e.g., LIBOR) due to an absence of liquidity in the market. The modelling framework is of "reduced form" in the sense that (similar to the credit risk literature) the source of credit risk is not modelled (nor is the source of liquidity risk). However, the framework has more structure than the literature seeking to simply model a different term structure of interest rates for each tenor frequency, since relationships between rates for all tenor frequencies are established based on the modelled roll-over risk. We proceed to consider a specific case within this framework, where the dynamics of interest rate and roll-over risk are driven by a multifactor Cox/Ingersoll/Ross-type process, show how such model can be calibrated to market data, and used for relative pricing of interest rate derivatives, including bespoke tenor frequencies not liquidly traded in the market.

Keywords: tenor swap, basis, frequency basis, liquidity risk, swap market

JEL Classification: C6, C63, G1, G13

Suggested Citation

Alfeus, Mesias and Grasselli, Martino and Schloegl, Erik, A Consistent Stochastic Model of the Term Structure of Interest Rates for Multiple Tenors (May 22, 2017). FIRN Research Paper, Available at SSRN: https://ssrn.com/abstract=2972428 or http://dx.doi.org/10.2139/ssrn.2972428

Mesias Alfeus

Department of Statistics and Actuarial Science - Stellenbosch University ( email )

Matieland
m
Stellenbosch, 7602
South Africa
0633236629 (Phone)
7405 (Fax)

Martino Grasselli

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

Erik Schloegl (Contact Author)

University of Technology Sydney (UTS), Quantitative Finance Research Centre ( email )

Ultimo
PO Box 123
Sydney, NSW 2007
Australia
+61 2 9514 2535 (Phone)

HOME PAGE: http://www.schlogl.com

University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management ( email )

Leslie Commerce Building
Rondebosch
Cape Town, Western Cape 7700
South Africa

Faculty of Science, Department of Statistics, University of Johannesburg ( email )

Auckland Park, 2006
South Africa

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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