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Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce


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Volume 18, Issue 1

Issues

A tractable model for indices approximating the growth optimal portfolio

Jan Baldeaux / Katja Ignatieva
  • School of Risk and Actuarial Studies, Australian School of Business, University of New South Wales, Sydney, Australia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Eckhard Platen
  • Finance Discipline Group and School of Mathematical Studies, University of Technology Sydney, Sydney, Australia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-02-04 | DOI: https://doi.org/10.1515/snde-2012-0054

Abstract

The growth optimal portfolio (GOP) plays an important role in finance, where it serves as the numéraire portfolio, with respect to which contingent claims can be priced under the real world probability measure. This paper models the GOP using a time dependent constant elasticity of variance (TCEV) model. The TCEV model has high tractability for a range of derivative prices and fits well the dynamics of a global diversified world equity index. This is confirmed when pricing and hedging various derivatives using this index.

This article offers supplementary material which is provided at the end of the article.

Keywords: growth optimal portfolio; constant elasticity of variance model; kernel estimation; diffusion coefficient function; derivative hedging

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About the article

Corresponding author: Jan Baldeaux, Finance Discipline Group, University of Technology Sydney, Australia, e-mail:


Published Online: 2014-02-04

Published in Print: 2014-02-01

Published in Print: 2014-02-01


Proceeding in this way appears to be the most straightforward way to estimate αt, which is required to obtain a stationary process

We cannot apply the same methodology as in the case of the MMM (where parameters
and c=1 are fixed). In our case the quadratic variation does not only depend on αt.

When estimating the diffusion coefficient function, we discard observations above the 90% quantile due to the fact that the probability distribution has a long right tail, indicating that there is not much data available to estimate reliably the diffusion coefficient function in the upper tail. Thus, we estimate the diffusion coefficient function from the truncated distribution.

One can also derive explicit pricing formulas for call and put options with strike price K. However, this would require us to make an explicit assumption regarding the short rate dynamics. The presented pricing problem avoids such an assumption.

We have also studied the hedging of call options, but omit the results from the paper since the hedge performance is similar to that of a put.

Hedging performance has also been tested using diversified indices on a monthly basis, such as, e.g., the S&P 500. The results are qualitatively similar to those obtained using daily data for the EWI114 as GOP and thus, are not presented in the paper.

Results for in-the-money and out-of-the-money options are similar, and thus, are not presented here.


Citation Information: Studies in Nonlinear Dynamics and Econometrics, Volume 18, Issue 1, Pages 1–21, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2012-0054.

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