Incomplete Continuous-time Securities Markets with Stochastic Income Volatility

Peter Ove Christensen, Kasper Larsen

Research output: Contribution to journalJournal articleResearchpeer-review

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 to the equilibrium in an otherwise identical complete market.
Original languageEnglish
JournalThe Review of Asset Pricing Studies
Volume4
Issue number2
Pages (from-to)247-285
Number of pages39
ISSN2045-9920
DOIs
Publication statusPublished - 2014
Externally publishedYes

Bibliographical note

Campus adgang til artiklen / Campus access to the article

Cite this

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Incomplete Continuous-time Securities Markets with Stochastic Income Volatility. / Christensen, Peter Ove; Larsen, Kasper.

In: The Review of Asset Pricing Studies, Vol. 4, No. 2, 2014, p. 247-285.

Research output: Contribution to journalJournal articleResearchpeer-review

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T1 - Incomplete Continuous-time Securities Markets with Stochastic Income Volatility

AU - Christensen, Peter Ove

AU - Larsen, Kasper

N1 - Campus adgang til artiklen / Campus access to the article

PY - 2014

Y1 - 2014

N2 - 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 to the equilibrium in an otherwise identical complete market.

AB - 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 to the equilibrium in an otherwise identical complete market.

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DO - 10.1093/rapstu/rau004

M3 - Journal article

VL - 4

SP - 247

EP - 285

JO - The Review of Asset Pricing Studies

JF - The Review of Asset Pricing Studies

SN - 2045-9920

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