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Polynomial term structure models

Objective

"The term structure of interest rates plays a central role in the functioning of the interbank market. It also represents a key factor for the valuation and management of long term liabilities, such as pensions. The financial crisis has revealed the multivariate risk nature of the term structure, which includes inflation, credit and liquidity risk, resulting in multiple spread adjusted discount curves. This has generated a strong interest in tractable stochastic models for the movements of the term structure that can match all determining risk factors.

We propose a new class of term structure models based on polynomial factor processes which are defined as jump-diffusions whose generator leaves the space of polynomials of any fixed degree invariant. The moments of their transition distributions are polynomials in the initial state. The coefficients defining this relationship are given as solutions of a system of nested linear ordinary differential equations. As a consequence polynomial processes yield closed form polynomial-rational expressions for the term structure of interest rates. Polynomial processes include affine processes, whose transition functions admit an exponential-affine characteristic function. Affine processes are among the most widely used models in finance to date, but come along with some severe specification limitations. We propose to overcome these shortcomings by studying polynomial processes and polynomial expansion methods achieving a comparable efficiency as Fourier methods in the affine case.

In sum, the objectives of this project are threefold. First, we plan to develop a theory for polynomial processes and entirely explore their statistical properties. This fills a gap in the literature on affine processes in particular. Second, we aim to develop polynomial-rational term structure models addressing the new paradigm of multiple spread adjusted discount curves. Third, we plan to implement and estimate these models using real market data."

Field of science

  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations
  • /social sciences/economics and business/business and management/commerce

Call for proposal

ERC-2012-StG_20111012
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Address
Batiment Ce 3316 Station 1
1015 Lausanne
Switzerland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 995 155
Principal investigator
Damir Filipovic (Prof.)
Administrative Contact
Caroline Vandevyver (Ms.)

Beneficiaries (1)

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Switzerland
EU contribution
€ 995 155
Address
Batiment Ce 3316 Station 1
1015 Lausanne
Activity type
Higher or Secondary Education Establishments
Principal investigator
Damir Filipovic (Prof.)
Administrative Contact
Caroline Vandevyver (Ms.)