Complete Models with Stochastic Volatility

David G. Hobson and L. C. G. Rogers

Mathematical Finance, 1998, vol. 8, issue 1, 27-48

Abstract: The paper proposes an original class of models for the continuous‐time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log‐price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference‐independent options prices. We find a partial differential equation for the price of a European call option. Smiles and skews are found in the resulting plots of implied volatility.

Date: 1998
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (85)

Downloads: (external link)
https://doi.org/10.1111/1467-9965.00043

Related works:
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:bla:mathfi:v:8:y:1998:i:1:p:27-48

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0960-1627

Access Statistics for this article

Mathematical Finance is currently edited by Jerome Detemple

More articles in Mathematical Finance from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().