A Hybrid Model for Equity Indices and Stochastic Interest Rates

32 Pages Posted: 10 Nov 2012 Last revised: 15 Sep 2013

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: September 15, 2013

Abstract

The growth optimal portfolio (GOP) plays an important role in finance, in particular in derivative pricing, where it is employed as a num\'eraire portfolio, allowing to price contingent claims directly under the real world probability measure. This paper derives an extension of a time dependent constant elasticity of variance (TCEV) model which takes into account stochastic interest rate risk. 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. Taking interest rate dynamics into account, we show that the hybrid model remains highly tractable and fits well the observed dynamics of diversified equity indices and interest rates. Our results are important for pricing and hedging of various derivative products, allowing to derive closed-form solutions for standard derivatives. Across all models under consideration we find that the hybrid model with 3/2 dynamics for the interest rate provides the best fit to the data. It leads to the lowest prices and the least expensive hedges.

Keywords: growth optimal portfolio, time dependent constant elasticity of variance model, nonparametric kernel

JEL Classification: C13, C14, G1

Suggested Citation

Baldeaux, Jan F. and Fung, Man Chung and Ignatieva, Katja and Platen, Eckhard, A Hybrid Model for Equity Indices and Stochastic Interest Rates (September 15, 2013). Available at SSRN: https://ssrn.com/abstract=2173273 or http://dx.doi.org/10.2139/ssrn.2173273

Jan F. Baldeaux

Standard Chartered Bank ( email )

United States

Man Chung Fung

Commonwealth Bank of Australia

CBP
Sydney, NSW 2064
Australia

Katja Ignatieva (Contact Author)

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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