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Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility

Author

Listed:
  • Peter O. Christensen
  • Kasper Larsen

Abstract

We derive closed-form solutions for the equilibrium interest rate and market price of risk processes in an incomplete continuous-time market with uncertainty generated by Brownian motions. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously. Countercyclical stochastic income volatility generates a countercyclical equilibrium market price of risk process and a procyclical equilibrium interest rate process. We show that when the investors’ unspanned income volatility is countercyclical, the resulting equilibrium displays both lower interest rates and higher risk premia compared with the equilibrium in an otherwise identical complete market.

Suggested Citation

  • Peter O. Christensen & Kasper Larsen, 2014. "Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 4(2), pages 247-285.
    • Handle: RePEc:oup:rasset:v:4:y:2014:i:2:p:247-285.
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    File URL: http://hdl.handle.net/10.1093/rapstu/rau004
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    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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