Non-Redundant Derivatives in a Dynamic General Equilibrium Economy

53 Pages Posted: 20 Mar 2002

See all articles by Harjoat Singh Bhamra

Harjoat Singh Bhamra

Imperial College Business School

Leonid Kogan

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER)

Raman Uppal

EDHEC Business School; Centre for Economic Policy Research (CEPR)

Date Written: July 2002


In this article, we wish to understand: (i) the valuation of a non-redundant derivative in an economy where agents are heterogenous, (ii) the role of such a derivative in an investor's dynamic portfolio strategy, and (iii) the effect of introducing this derivative on the prices of more primitive securities, such as a stock and bond. We do this by studying a dynamic general equilibrium exchange economy in continuous time with two agents who differ in their degree of risk aversion, and where both the endowment and its growth rate are stochastic. We study two versions of this economy: in the first, only a stock and a zero-supply instantaneously riskless bond are available for trading, so that financial markets are incomplete; in the second version of this economy, we introduce a derivative that allows the agent to hedge perfectly the risk arising from the stochastic growth rate of endowment. Our main contribution is to characterize in closed form (using asymptotic analysis) the equilibrium in these two versions of the economy, including an expression for the price of the derivative in the second economy. We then compare analytically the portfolio policies and prices across the two versions of the economy. We find that the introduction of a derivative leads to an increase in the interest rate, expected return on the stock and the volatility of stock returns.

Keywords: Asset pricing, derivative valuation, portfolio choice, incomplete markets

JEL Classification: G12, G11, D52

Suggested Citation

Bhamra, Harjoat Singh and Kogan, Leonid and Uppal, Raman, Non-Redundant Derivatives in a Dynamic General Equilibrium Economy (July 2002). London Business School Working Paper; EFA 2002 Berlin Meetings Presented Paper, Sauder School of Business Working Paper, Available at SSRN: or

Harjoat Singh Bhamra (Contact Author)

Imperial College Business School ( email )

Tanaka Building
Exhibition Rd
London, SW7 2AZ
United Kingdom


Leonid Kogan

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
Cambridge, MA 02142
United States
617-253-2289 (Phone)
617-258-6855 (Fax)


National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

Raman Uppal

EDHEC Business School ( email )

58 rue du Port
Lille, 59046

Centre for Economic Policy Research (CEPR)

90-98 Goswell Road
London, EC1V 7RR
United Kingdom

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