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Market Resolution and Valuation in Incomplete Markets

Published online by Cambridge University Press:  06 April 2009

Kose John
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Extract

The Arrow-Debreu approach to general equilibrium in an economy has been recognized as one of the most general and conceptually elegant frameworks for the study of financial problems under uncertainty [2], [9]. Equally well known is its elusiveness when it comes to ready application to practical problems (like capital budgeting) or empirical testing. (See [6], [15]–[18].) However, some recent research (see [1], [3], [6], [12]–[16], [18], and [19]) has made a serious attempt to put the state-preference theoretic model in an operational setting. Breeden and Litzenberger [6] have developed an interesting approach to derive constructively the prices of elementary Arrow-Debreu securities from the prices of call options on aggregate consumption. Banz and Miller [3] use a similar technique to value capital budgeting projects based on values for state-contingent claims computed from prices of call options written on the market portfolio. The “supershare” securities proposed by Hakansson [14]–[16] and related work by Garman [13], Ross [24], etc., have also served to give the so-called “state-contingent” approach a practical flavor.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 19 , Issue 1 , March 1984 , pp. 29 - 44
Copyright
Copyright © School of Business Administration, University of Washington 1984

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References

[1]Arditti, F. D., and John, K.. “Spanning the State Space with Options.” Journal of Financial and Quantitative Analysis, Vol. 15 (03 1980), pp. 1–9.CrossRefGoogle Scholar
[2]Arrow, K. J. “The Role of Securities in the Optimal Allocation of Risk-Bearing.” Review of Economic Studies, Vol. 31 (1963–1964), pp. 91–96.CrossRefGoogle Scholar
[3]Banz, R. W., and Miller, M. H.. “Prices for State-Contingent Claims: Some Estimates and Application.” Journal of Business, Vol. 51 (10 1978), pp. 653–672.CrossRefGoogle Scholar
[4]Black, F. “The Pricing of Complex Options and Corporate Liabilities.” Mimeographed. Chicago: University of Chicago (1974).Google Scholar
[5]Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (05/06 1973), pp. 637–654.CrossRefGoogle Scholar
[6]Breeden, D. T., and Litzenberger, R. H.. “Prices of State-Contingent Claims Implicit in Option Prices.” Journal of Business, Vol. 51 (10 1978), pp. 621–651.CrossRefGoogle Scholar
[7]Brennan, M. J. “The Pricing of Contingent Claims in Discrete Time Models.” The Journal of Finance, Vol. 2 (03 1979), pp. 53–68.CrossRefGoogle Scholar
[8]Brennan, M. J., and Solanki, R.. ”Optimal Portfolio Insurance.” Working Paper No. 666, Faculty of Commerce and Business Administration, University of British Columbia (1979).Google Scholar
[9]Debreu, G.Theory of Value. New Haven and London: Yale University Press (1959).Google Scholar
[10]Ekern, S., and Wilson, R. B.. “On the Theory of the Firm in an Economy with Incomplete Markets.” The Bell Journal of Economics and Management Science, Vol. 5 (Spring 1974), pp. 171–180.CrossRefGoogle Scholar
[11]Friesen, P. H. “A Reinterpretation of the Equilibrium Theory of Arrow and Debreu in Terms of Financial Markets.” Technical Report No. 126, Institute for Mathematical Studies in the Social Sciences, Stanford University (1974).Google Scholar
[12]Friesen, P. H. “The Arrow-Debreu Model Extended to Financial Markets.” Econometrica, Vol. 47 (05 1979), pp. 689–707.CrossRefGoogle Scholar
[13]Garman, M. B. “The Pricing of Supershares.” Journal of Financial Economics, Vol. 6 (03 1978), pp. 3–10.CrossRefGoogle Scholar
[14]Hakansson, N. H. “The Purchasing Power Fund: A New Kind of Financial Intermediary.” Financial Analysts Journal, Vol. 32 (11/12 1976), pp. 2–12.CrossRefGoogle Scholar
[15]Hakansson, N. H. “Efficient Paths Toward Efficient Capital Markets in Large and Small Countries.” In Financial Decision Making under Uncertainty, Levy, H. and Sarnat, M., eds. New York: Academic Press (1977).Google Scholar
[16]Hakansson, N. H. “Welfare Aspects of Options and Supershares.” The Journal of Finance, Vol. 35 (06 1978), pp. 759–776.CrossRefGoogle Scholar
[17]Hirshleiffer, J. H.Investment, Interest and Capital. Englewood Cliffs, N.J.: Prentice-Hall (1974).Google Scholar
[18]John, K. “Efficient Funds in Financial Markets with Options: A New Irrelevance Proposition.” The Journal of Finance, Vol. 37 (06 1981), pp. 685–695.CrossRefGoogle Scholar
[19]Kreps, D. M. “Multiperiod Securities and the Efficient Allocation of Risk: A Comment on the Black-Scholes Option Pricing Model.” In The Economics of Information and Uncertainty, McCall, J. J., ed. Chicago: University of Chicago Press (1982).Google Scholar
[20]Hart, O. D. “On the Existence of Equilibrium in a Securities Model.” Journal of Economic Theory, Vol. 9 (04 1975), pp. 293–311.CrossRefGoogle Scholar
[21]Hart, O. D. “On the Optimality of Equilibrium When the Market Structure is Incomplete.” Journal of Economic Theory, Vol. 11 (12 1975), pp. 418–443.CrossRefGoogle Scholar
[22]Radner, R. “Competitive Equilibrium under Uncertainty.” Econometrica, Vol. 36 (01 1968), pp. 31–58.CrossRefGoogle Scholar
[23]Radner, R. “A Note on Unanimity of Stockholders' Preferences among Alternative Production Plans: A Reformulation of the Ekern-Wilson Model.” The Bell Journal of Economics and Management Science, Vol. 5 (Spring 1974), pp. 181–184.CrossRefGoogle Scholar
[24]Ross, S. A. “Options and Efficiency.” Quarterly Journal of Economics, Vol. 90 (02 1976), pp. 75–89.CrossRefGoogle Scholar
[25]Royden, H. L.Real Analysis, 2nd ed. New York: Macmillan (1968).Google Scholar
[26]Satterthwaite, M. A. “On the Scope of the Stockholder Unanimity Theorems.” International Economic Review, Vol. 22 (02 1981), pp. 119–133.CrossRefGoogle Scholar