A Practical Robust Long Term Yield Curve Model

High Performance Computing in Finance, J Kanniainen, J Keane and E Vynckier, eds. Chapman & Hall CRC Financial Mathematics Series (2015), Forthcoming

49 Pages Posted: 2 Jul 2015 Last revised: 26 Jan 2016

See all articles by M. A. H. Dempster

M. A. H. Dempster

University of Cambridge - Centre for Financial Research; Cambridge Systems Associates Limited; University of Cambridge - Judge Business School

Elena Medova

University of Cambridge - Centre for Financial Research; Cambridge Systems Associates Limited

Igor Osmolovskiy

Cambridge Systems Associates Limited

Philipp Ustinov

Cambridge Systems Associates Limited

Date Written: June 25, 2015

Abstract

This paper describes the development and initial testing of the Black-corrected version of a workhorse 3-factor Gaussian yield curve (term structure) model, the economic factor model (Dempsteret al., 2010) which we have used for many years with Monte Carlo scenario simulation for structured derivative valuation, investment modelling and asset liability management with various time steps and currencies. In common with most alternative approaches in the literature to generating non-negative yieldsusing Black's idea, we propose a simple approximation to the Black mathematical model using the nonlinear unscented Kalman filter (UKF). However, model calibration, unlike that of the current computationally intensive alternatives, requires not significantly more computing time than is needed for the linear Kalman filter with the underlying affine shadow rate model. Initial empirical testing of the new Black EFM model both in- and out-of-sampleshows acceptable accuracy, improved over that of the affine EFM model, which can be further improved by UKF tuning in future research. Migration of the system to the cloud can reduce calibration times for both models from a few hours to a few minutes by exploiting massive parallelization of the computationally intensive step.

Keywords: yield curve, Gaussian affine models, Black correction, nonnegative rates, unscented Kalman filter, long term Monte Carlo simulation

JEL Classification: E43, E44, E47

Suggested Citation

Dempster, M. A. H. and Medova, Elena and Osmolovskiy, Igor and Ustinov, Philipp, A Practical Robust Long Term Yield Curve Model (June 25, 2015). High Performance Computing in Finance, J Kanniainen, J Keane and E Vynckier, eds. Chapman & Hall CRC Financial Mathematics Series (2015), Forthcoming. Available at SSRN: https://ssrn.com/abstract=2625185 or http://dx.doi.org/10.2139/ssrn.2625185

M. A. H. Dempster (Contact Author)

University of Cambridge - Centre for Financial Research ( email )

Centre for Mathematical Sciences
Wilberforce Road
Cambridge, CB3 0WA
United Kingdom

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

University of Cambridge - Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom

Elena Medova

University of Cambridge - Centre for Financial Research ( email )

Centre for Mathematical Sciences
Wilberforce Road
Cambridge, CB3 0WA
United Kingdom

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

Igor Osmolovskiy

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

Philipp Ustinov

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

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