THE SQUARED ORNSTEIN‐UHLENBECK MARKET

J. Aquilina and L. C. G. Rogers

Mathematical Finance, 2004, vol. 14, issue 4, 487-513

Abstract: We study a complete market containing J assets, each asset contributing to the production of a single commodity at a rate that is a solution to the squared Ornstein‐Uhlenbeck (Cox‐Ingersoll‐Ross) SDE. The assets are owned by K agents with CRRA utility functions, who follow feasible consumption/investment regimes so as to maximize their expected time‐additive utility from consumption. We compute the equilibrium for this economy and determine the state‐price density process from market clearing. Reducing to a single (representative) agent, and exploiting the relation between the squared‐OU and squared‐Bessel SDEs, we obtain closed‐form expressions for the values of bonds, assets, and options on the total asset value. Typical model parameters are estimated by fitting bond price data, and we use these parameters to price the assets and options numerically. Implications for the total asset price itself as a diffusion are discussed. We also estimate implied volatility surfaces for options and bond yields.

Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1111/j.0960-1627.2004.00202.x

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:14:y:2004:i:4:p:487-513

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 ().