Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility

40 Pages Posted: 18 Mar 2011 Last revised: 27 Apr 2013

See all articles by Peter O. Christensen

Peter O. Christensen

Copenhagen Business School - Department of Finance

Kasper Larsen

Rutgers, The State University of New Jersey

Date Written: April 26, 2013

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, 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.

Keywords: Incomplete markets, non-Pareto efficiency, stochastic volatility, stochastic interest rates, stochastic risk premia

Suggested Citation

Christensen, Peter Ove and Larsen, Kasper, Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility (April 26, 2013). Available at SSRN: https://ssrn.com/abstract=1786606 or http://dx.doi.org/10.2139/ssrn.1786606

Peter Ove Christensen (Contact Author)

Copenhagen Business School - Department of Finance ( email )

Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark
+45 6140 3237 (Phone)

Kasper Larsen

Rutgers, The State University of New Jersey ( email )

311 North 5th Street
New Brunswick, NJ 08854
United States

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