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05-08-2023 | Notes and Short Article

Banks and Markets from an Insurance Perspective

Authors: Amaury Goguel, Maxence Miéra

Published in: Journal of Quantitative Economics | Issue 4/2023

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Abstract

This article aims to clarify the analogy between contingent claims in a complete market and banking contracts in a capitalized financial intermediary that combines both deposit and equity. It brings together insurance theory and financial intermediation theory in a synthetic model by focusing on the risk allocation function rather than on a particular kind of institutional arrangement. The model includes both idiosyncratic liquidity risk and aggregate uncertainty on asset return, and it focuses on risk allocation in a perfect information setting from an insurance perspective. This article then highlights that equity contracts are equivalent to state-contingent claims in the aggregate-risk shifting, that deposit contracts are equivalent to type-contingent claims in the idiosyncratic-risk mutualization, and that banks and markets both implement the optimal allocation by simply using different mechanisms.

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See Allen and Santomero (1997) for a critical view of this approach. They notably point out that: "The literature’s emphasis on the role of intermediaries as reducing the frictions of transaction costs and asymmetric information is too strong. (...) Risk management has become a key area of intermediary activity, though intermediation theory has offered little to explain why institutions should perform this function" (p. 1462).

The framework constitutes a variation on Diamond and Dybvig (1983). This variation is close to that of Allen and Gale (2004). The main difference is that liquidity shocks are assumed to be observable for the purpose of analysis.

See Judd (1985) regarding the application of the law of large numbers in a continuum.

As $\pi _s / p_s$ is a constant, we can express all prices with respect to a reference state k:

$$\begin{aligned} \forall s, \quad p_s = \pi _s \frac{p_k}{\pi _k}. \end{aligned}$$

It follows that

$$\begin{aligned} \sum _s p_s (W_{2s}^{A*} - R_s) = \frac{p_k}{\pi _k} \sum _s \pi _s (W_{2s}^{A*} - R_s) = 0, \end{aligned}$$

which can be rewritten as

$$\begin{aligned} \sum _s \pi _s W_{2s}^{A*} = \sum _s \pi _s R_s. \end{aligned}$$

We assumed that the coefficient of risk aversion of consumers was greater than unity: $-C u_C''(C) / u_C'(C) >1$. This can be rewritten as follows: $u_C'(C) + C u_C'' (C) <0$, or $\partial C u_C'(C) / \partial C < 0$.

Note that $\sum \pi _s u_I(B_s^I) = u_I(\sum \pi _s B_s^I)$ and that $u_I(\sum \pi _s B_s^I) \ge u_I(E(R))$ if and only if $\sum \pi _s B_s^I \ge E(R)$.

The determination of the optimality conditions is less direct than for the other programs. We focus here on the main features from an economic perspective and provide technical details in the Appendix.

Financial intermediaries can mutualize and reduce transaction costs (Benston and Smith 1976). They can produce information (Fama 1985). They can also deal efficiently with private information (Diamond and Dybvig 1983), contract incompleteness (Allen and Gale 2004), or agency problems (Townsend 1979; Diamond 1984).

Allen, F., and D. Gale. 2003. Capital adequacy regulation: In search of a rationale. In Economics in an imperfect world: Essays in honor of Joseph Stiglitz, ed. R. Arnott, B. Greenwald, R. Kanbur, and B. Nalebuff, 83–109. MIT Press.CrossRef

Allen, F., and D. Gale. 2004. Financial intermediaries and markets. Econometrica 72 (4): 1023–1061.CrossRef

Allen, F., and A. Santomero. 1997. The theory of financial intermediation. Journal of Banking & Finance 21 (11–12): 1461–1485.CrossRef

Arrow, K. 1953. Le rôle des valeurs boursières pour la répartition la meilleure des risques. Colloques Internationaux du Centre National de la Recherche Scientifique, 11:41–47. Translated (1964) as "The role of securities in the optimal allocation of risk– bearing", Review of Economic Studies, 31(2):91–96.

Benston, G., and C. Smith. 1976. A transactions cost approach to the theory of financial intermediation. Journal of Finance 31 (2): 215–231.CrossRef

Borch, K. 1962. Equilibrium in a reinsurance market. Econometrica 30 (3): 424–444.CrossRef

Diamond, D. 1984. Financial intermediation and delegated monitoring. Review of Economic Studies 51 (3): 393–414.CrossRef

Diamond, D., and P. Dybvig. 1983. Bank runs, deposit insurance, and liquidity. Journal of Political Economy 91 (3): 401–419.CrossRef

Dionne, G. 2013. Handbook of insurance. Springer.CrossRef

Doherty, N., and H. Schlesinger. 1985. Incomplete markets for insurance: An overview. Journal of Risk and Insurance 52 (3): 402–423.CrossRef

Fama, E. 1985. What’s different about banks? Journal of Monetary Economics 15 (1): 29–39.CrossRef

Freixas, X., and J.-C. Rochet. 2008. Microeconomics of banking. MIT press.

Gale, D. 2003. Financial regulation in a changing environment. In Framing financial structure in an information environment, ed. T. Courchene and E. Neave. John Deutsch Institute for the Study of Economic Policy: Queen’s University.

Gorton, G., and G. Pennacchi. 1990. Financial intermediaries and liquidity creation. Journal of Finance 45 (1): 49–71.CrossRef

Hirshleifer, J., and J. Riley. 1979. The analytics of uncertainty and information: An expository survey. Journal of Economic Literature 17 (4): 1375–1421.

Judd, K. 1985. The law of large numbers with a continuum of IID random variables. Journal of Economic Theory 35 (1): 19–25.CrossRef

Townsend, R. 1979. Optimal contracts and competitive markets with costly state verification. Journal of Economic Theory 21 (2): 265–293.CrossRef

Title: Banks and Markets from an Insurance Perspective
Authors: Amaury Goguel
Maxence Miéra
Publication date: 05-08-2023
Publisher: Springer India
Published in: Journal of Quantitative Economics / Issue 4/2023
Print ISSN: 0971-1554
Electronic ISSN: 2364-1045
DOI: https://doi.org/10.1007/s40953-023-00365-8

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