A Benchmark Approach To Finance
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Wiley Blackwell in its journal Mathematical Finance.
Volume (Year): 16 (2006)
Issue (Month): 1 ()
Contact details of provider:
Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627
Other versions of this item:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- David Heath & Eckhard Platen, 2004.
"Understanding the Implied Volatility Surface for Options on a Diversified Index,"
Research Paper Series
128, Quantitative Finance Research Centre, University of Technology, Sydney.
- David Heath & Eckhard Platen, 2004. "Understanding the Implied Volatility Surface for Options on a Diversified Index," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 55-77, March.
- Eckhard Platen, 2001.
"A Minimal Financial Market Model,"
Research Paper Series
48, Quantitative Finance Research Centre, University of Technology, Sydney.
- Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
- I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 291-309.
- Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney.
- Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
- Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
- Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
- Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
- L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176.
- Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.