Carnegie Mellon University
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Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility

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journal contribution
posted on 2013-04-01, 00:00 authored by Peter O. Christensen, Kasper LarsenKasper Larsen

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, and we show that when the investors’ unspanned income volatility is countercyclical, the resulting equilibrium displays both lower interest rates and higher risk premia compared to the equilibrium in an otherwise identical complete market.


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© The Author 2014. This is an electronic version of an article published by Oxford University Press. The version of record is available online at