A Benchmark Approach to Finance

Eckhard Platen (eckhard.platen@uts.edu.au)

No 138, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper derives a unified framework for portfolio optimization, derivative pricing, financial modeling and risk measurement. It is based on the natural assumption that investors prefer more or less, in the sense that the higher drift is preferred. Each such investor is shown to hold an efficient portfolio in the sense of Markowitz with units in the market portfolio and the savings account of his or her home currency. If the market portfolio is diversified or monetary authorities aim to maximize the growth rates of the portfolios of their market participants through corresponding interest policies, then the market portfolio is the growth optimal portfolio (GOP). In this setup the capital asset pricing model follows without the use of expected utility functions or equilibrium assumptions. The expected increase of the discounted value of GOP is shown to coincide with the expected increase of its discounted underlying value. The discounted GOP has the dynamics of a time transformed squared Bessel process of dimension four. The time transformation is given by the discounted underlying value of the GOP. The squared volatility of the GOP equals the discounted GOP drift, when expressed in units of the discounted GOP. Risk neutral derivative pricing and actuarial pricing are generalized by the fair pricing concept, which uses the GOP as numeraire and the real world probability measure as pricing measure. An equivalent risk neutral martingale measure does not exist under the derived minimal market model.

Keywords: benchmark model; market portfolio; growth optimal portfolio; efficient frontier; captal asset pricing model; fair pricing; stochastic volatility; minimal market model (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2004-10-01
New Economics Papers: this item is included in nep-cfn, nep-fin and nep-ifn
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (107)

Published as: Platen, E., 2006, "A Benchmark Approach to Finance", Mathematical Finance, 16(1), 131-151.

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Related works:
Journal Article: A BENCHMARK APPROACH TO FINANCE (2006)
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