A Hybrid Model for Pricing and Hedging of Long Dated Bonds

29 Pages Posted: 13 Mar 2015 Last revised: 30 Sep 2015

See all articles by Jan F. Baldeaux

Jan F. Baldeaux

Standard Chartered Bank

Simon Man Chung Fung

Commonwealth Bank of Australia

Katja Ignatieva

University of New South Wales - Australian School of Business

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Date Written: April 24, 2015

Abstract

Long dated fixed income securities play an important role in asset-liability management, in life insurance and in annuity businesses. This paper applies the benchmark approach, where the growth optimal portfolio (GOP) is employed as numeraire together with the real world probability measure for pricing and hedging of long dated bonds. It employs a time dependent constant elasticity of variance model for the discounted GOP and takes stochastic interest rate risk into account. This results in a hybrid framework that models the stochastic dynamics of the GOP and the short rate simultaneously. We estimate and compare a variety of continuous-time models for short-term interest rates using non-parametric kernel-based estimation. The hybrid models remain highly tractable and fit reasonably well the observed dynamics of proxies of the GOP and interest rates. Our results involve closed-form expressions for bond prices and hedge ratios. Across all models under consideration we find that the hybrid model with the 3/2 dynamics for the interest rate provides the best fit to the data with respect to lowest prices and least expensive hedges.

Keywords: Long dated bond pricing, stochastic interest rate, growth optimal portfolio, nonparametric kernel

Suggested Citation

Baldeaux, Jan F. and Fung, Man Chung and Ignatieva, Katja and Platen, Eckhard, A Hybrid Model for Pricing and Hedging of Long Dated Bonds (April 24, 2015). UNSW Business School Research Paper No. 2015ACTL06. Available at SSRN: https://ssrn.com/abstract=2577062 or http://dx.doi.org/10.2139/ssrn.2577062

Jan F. Baldeaux (Contact Author)

Standard Chartered Bank ( email )

United States

Man Chung Fung

Commonwealth Bank of Australia

CBP
Sydney, NSW 2064
Australia

Katja Ignatieva

University of New South Wales - Australian School of Business ( email )

UNSW Business School
High St
Sydney, NSW 2052
Australia

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

Broadway
GPO Box 123
Sydney, NSW 2007, 2007
Australia
+61 2 9514 7759 (Phone)

HOME PAGE: http://datasearch.uts.edu.au/business/finance/staff/StaffDetails.cfm?UnitStaffId=90

University of Technology Sydney, School of Mathematical and Physical Sciences ( email )

P.O. Box 123
Broadway
Sydney, New South Wales 2007
Australia
+61 (02) 9514 2271 (Phone)

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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