Abstract
Financial primitives are introduced to define acceptable loss exposures when demands and supplies are defined on differing event spaces. Acceptable loss exposures are modeled by a convex cone of random variables containing the nonnegative random variables. The resulting financial equilibrium defines in general a two price economy. Analytical procedures for identifying the two prices are described. The size of the two price economy is fundamentally determined by the financial system that determines the size of the cone of acceptable losses. There are implications for accounting and risk management as liabilities would typically be valued at ask while assets are valued at bid with no data available on bidirectional prices for anything. Marking to market in such financial economies is at best marking to two price economies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amihud Y., Mendelson H.: Dealership market: market making with inventory. J Financ Econ 8, 31–53 (1980)
Arrow K.J., Debreu G.: Existene of equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)
Arrow K.J.: The role of securities in the optimal allocation of risk bearing. Rev Econ Stud 31, 91–96 (1964)
Artzner P., Delbaen F., Eber J.M., Heath D.: Coherent measures of risk. Math Financ 9, 203–228 (1999)
Bernardo A., Ledoit O.: Gain, loss, and asset pricing. J Polit Econ 108, 144–172 (2000)
Carr P., Geman H., Madan D.: Pricing and hedging in incomplete markets. J Financ Econ 62, 131–167 (2001)
Černý A., Hodges S.: The theory of good deal pricing in financial markets. In: Geman, H., Madan, D., Pliska, S.R., Vorst, T. (eds) Mathematical Finance-Bachelier Congress 2000, Springer, Berlin (2000)
Choi J.Y., Salandro D., Shastri K.: On the estimation of bid-ask spreads: theory and evidence. J Financ Quant Anal 23, 219–230 (1988)
Cochrane J.H., Saá-Requejo J.: Beyond arbitrage: ‘good deal’ asset price bounds in incomplete markets. J Polit Econ 108, 79–119 (2000)
Copeland T.C., Galai D.: Information effects on the bid ask spread. J Financ 38, 1457–1469 (1983)
Debreu G.: Theory of Value. Wiley, New York (1959)
Demsetz H.: The cost of transacting. Q J Econ 82, 33–53 (1968)
Duffie D., Singleton K.: Credit Risk: Pricing, Measurement and Management. Princeton University Press, Princeton (2003)
Easley D., O’Hara M.: Price, trade size and information in securities markets. J Financ Econ 19, 69–90 (1987)
Eberlein, E., Madan, D.B.: Unlimited liabilities, reserve capital requirements and the taxpayer put option. Quant Financ (2011). doi:10.1080/14697688.2011630324
Flannery M., Kwan S.H., Nimalendran M.: The 2007–2009 Financial Crisis and Bank Opaquness. Working Paper, Federal Reserve Bank of San Francisco (2010)
Föllmer H., Schied A.: Stochastic Finance: An Introduction in Discrete Time, 2nd edn. Walter de Gruyter, Berlin (2004)
George T.J., Kaul G., Nimalendran M.: Estimation of the bid-ask spreads and its components: a new approach. Rev Financ Stud 4, 623–656 (1991)
Gilboa I., Schmeidler D.: Maxmin expected utility with non-unique prior. J Math Econ 18, 141–153 (1989)
Glosten L.R., Milgrom P.R.: Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. J Financ Econ 14, 71–100 (1985)
Gray, D.F., Merton, R.C., Bodie, Z.: New framework for measuring and managing macrofinancial risk and financial stability. Working Paper No. 09-015 (revised), Harvard Business School (2008)
Ho T., Stoll H.R.: Optimal dealer pricing under transactions and return uncertainty. J Financ Econ 9, 47–73 (1981)
Ho T., Stoll H.R.: The dynamics of dealer markets under competition. J Financ 38, 1053–1074 (1983)
Huang R.D., Stoll H.R.: The components of the bid ask spread: a general approach. Rev Financ Stud 10, 995–1034 (1997)
Ingersoll J.E. Jr.: Theory of Financial Decision Making. Rowman and Littlefield, New Jersey (1987)
Jaschke S., Kuchler U.: Coherent risk measures and good deal bounds. Financ Stochast 5, 181–200 (2001)
Kyle A.: Continuous auctions and insider trading. Econometrica 53, 1315–1335 (1985)
Madan, D.B.: On the Pricing of Contingent Convertible Notes. In: M. Kijima, Hara, C., Muromachi, Y., Nakaoka, H., Nishide, K. (eds.), Recent Advances in Financial Engineering. Singapore, World Scientific (forthcoming) (2012)
Madan, D.B., Schoutens, W.: Structured products equilibria in conic two price markets. Math Financ Econ (2012). doi:10.1007/s11579-012-0064-7
Merton R.C.: On the pricing of corporate debt: the risk structure of interest rates. J Financ 29, 449–470 (1974)
Merton R.C.: An analytic derivation of the cost of loan guarantees and deposit insurance: An application of modern option pricing theory. J Banking Financ 1, 3–11 (1977)
Roll R.: A simple implicit measure of the effective bid-ask spread in an efficient market. J Financ 39, 1127–1139 (1984)
Skiadas C.: Asset Pricing Theory. Princeton University Press, Princeton (2009)
Stoll H.R.: The supply of dealer services in securities markets. J Financ 33, 1133–1151 (1978)
Stoll H.R.: Inferring the components of the bid-ask spread: theory and empirical tests. J Financ 44, 115–134 (1989)
Author information
Authors and Affiliations
Corresponding author
Additional information
Research on this paper was partially supported by a grant from the Committee on the Theory of Risk of the Casualty Actuarial Society. I also thank Peter Carr, Freddy Delbaen, Richard Derrig, Ernst Eberlein, Thomas Gehrig, Phil Heckman, Ajay Khanna, Wim Schoutens, J.J. Vicente Alvarez, and Shaun Wang for helpful discussions on the subject matter of this paper.
Rights and permissions
About this article
Cite this article
Madan, D.B. A two price theory of financial equilibrium with risk management implications. Ann Finance 8, 489–505 (2012). https://doi.org/10.1007/s10436-012-0200-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10436-012-0200-7