Understanding the Implied Volatility Surface for Options on a Diversified Index

David Heath and Eckhard Platen ()

No 128, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: index derivatives; minimal market model; random scaling; growth optimal portfolio; fair pricing; binary options (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2004-06-01
New Economics Papers: this item is included in nep-ets and nep-fin
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published as: Heath, D. and Platen, E., 2004, "Understanding the Implied Volatility Surface for Options on a Diversified Indexs", Asia-Pacific Financial Markets, 11(1), 55-77.

Downloads: (external link)
http://www.qfrc.uts.edu.au/research/research_papers/rp128.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://www.qfrc.uts.edu.au/research/research_papers/rp128.pdf [301 Moved Permanently]--> http://www.uts.edu.au/node/51831 [301 Moved Permanently]--> https://www.uts.edu.au/node/51831)

Related works:
Journal Article: Understanding the Implied Volatility Surface for Options on a Diversified Index (2004)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:128

Access Statistics for this paper

More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford ().