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The Squared Ornstein‐Uhlenbeck Market

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  • J. Aquilina
  • L. C. G. Rogers

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

  • J. Aquilina & L. C. G. Rogers, 2004. "The Squared Ornstein‐Uhlenbeck Market," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 487-513, October.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:4:p:487-513
    DOI: 10.1111/j.0960-1627.2004.00202.x
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    References listed on IDEAS

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    1. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
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    Cited by:

    1. Huantian Xie & Nenghui Kuang, 2021. "Sequential Maximum Likelihood Estimation for the Squared Radial Ornstein-Uhlenbeck Process," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1409-1417, December.

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