This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Understanding the Implied Volatility Surface for Options on a Diversified Index

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
David Heath
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

Additional information is available for the following registered author(s):

Abstract

This paper describes a two-factor model for a diversifed index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market activity time where the discounted growth optimal portfolio is expressed as a time transformed squared Bessel process of dimension four. It turns out that for this index model an equivalent risk neutral martingale measure does not exist because the corresponding Radon-Nikodym derivative process is a strict local martingale. However, a consistent pricing and hedging framework is established by using the benchmark approach. The proposed model,which includes a random initial condition for market activity, generates implied volatility surfaces for European call and put options that are typically observed in real markets. The paper also examines the price differences of binary options for the proposed model and their Black-Scholes counterparts.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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.

File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp128.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 128.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 23
Date of creation: 01 Jun 2004
Date of revision:
Handle: RePEc:uts:rpaper:128

Contact details of provider:
Postal: PO Box 123, Broadway, NSW 2007, Australia
Phone: +61 2 9514 7777
Fax: +61 2 9514 7711
Web page: http://www.business.uts.edu.au/qfrc/index.html
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Duncan Ford).

Related research
Keywords: index derivatives; minimal market model; random scaling; growth optimal portfolio; fair pricing; binary options;

Other versions of this item:

Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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.:
  1. Wolfgang Breymann & Leah Kelly & Eckhard Platen, 2004. "Intraday Empirical Analysis and Modeling of Diversified World Stock Indices," Research Paper Series 125, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  2. Heynen, Ronald & Kemna, Angelien & Vorst, Ton, 1994. "Analysis of the Term Structure of Implied Volatilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 31-56, March. [Downloadable!]
  3. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, September.
  4. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  5. Joshua Rosenberg, 1999. "Implied Volatility Functions: A Reprise," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-027, New York University, Leonard N. Stern School of Business-. [Downloadable!]
  6. David Heath & S. Hurst & Eckhard Platen, 1999. "Modelling the Stochastic Dynamics of Volatility for Equity Indices," Research Paper Series 7, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July. [Downloadable!] (restricted)
  8. 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. [Downloadable!]
  9. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
    Other versions:
  10. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  11. Franks, Julian R & Schwartz, Eduardo S, 1991. "The Stochastic Behaviour of Market Variance Implied in the Prices of Index Options," Economic Journal, Royal Economic Society, vol. 101(409), pages 1460-75, November. [Downloadable!] (restricted)
  12. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 211-239, June. [Downloadable!]
  13. David Heath & Eckhard Platen, 2004. "Local Volatility Function Models under a Benchmark Approach," Research Paper Series 124, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
Full references

Cited by:
(explanations, 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.)

  1. Shane Miller & Eckhard Platen, 2004. "A Two-Factor Model for Low Interest Rate Regimes," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 107-133, March. [Downloadable!] (restricted)
    Other versions:
  2. David Heath & Eckhard Platen, 2005. "Currency Derivatives under a Minimal Market Model with Random Scaling," Research Paper Series 154, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  3. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
Statistics
Access and download statistics

Did you know? About 1000 journals are listed on RePEc.

This page was last updated on 2009-11-9.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.