The Squared Ornstein-Uhlenbeck Market

27 Pages Posted: 21 Sep 2004  

John Aquilina

University of Bath - School of Mathematical Sciences

L. C. G. Rogers

University of Cambridge - Centre for Mathematical Sciences

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.

Suggested Citation

Aquilina, John and Rogers, L. C. G., The Squared Ornstein-Uhlenbeck Market. Mathematical Finance, Vol. 14, No. 4, pp. 487-513, October 2004. Available at SSRN: https://ssrn.com/abstract=591375

John Aquilina (Contact Author)

University of Bath - School of Mathematical Sciences ( email )

Bath, BA2 7AY
United Kingdom

L. C. G. (Chris) Rogers

University of Cambridge - Centre for Mathematical Sciences ( email )

Cambridge, CB3 9DD
United Kingdom

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