International Review of Economics and Finance 9 2000 375–386
A contingent claim analysis of a rate-setting financial intermediary
Jyh-Horng Lin
Graduate Institute of International Business, Tamkang University, Tamsui Campus, Tamsui, Taipei, Taiwan Received 30 June 1998; revised 11 December 1998; accepted 24 February 1999
Abstract
Realizing that a financial intermediary’s lending, treated as an investment opportunity, is like a financial call option clarifies the role of uncertainty. We argue that the portfolio-
theoretic approach and the firm-theoretic approach have important linkages that can be used to demonstrate the contingent claim analysis of a rate-setting financial intermediary. Borrower-
intermediary-lender relationships between the portfolio-theoretic combined volatilities and the firm-theoretic rate-setting modes under the Black-Scholes valuation are investigated, and
the conclusions depend upon the portfolio composition redistribution effect. The effect of changes in the open market security rates on the loan rate and deposit rate settings depend
on the borrower-intermediary-lender relationship, portfolio risk, and management of rate- setting strategy. Moreover, movements in open market security rates are not necessarily
transmitted to the loan lender and deposit absorber.
2000 Elsevier Science Inc. All rights
reserved.
JEL classification: G13
Keywords: Black-Scholes valuation; Loan rate setting; Deposit rate setting
1. Introduction
Dealing with the analysis of the determinants of the prices of contingent claim assets whose value is a non-proportional function of the value of another asset, the
Black-Scholes option-pricing model basically utilizes the concept of the portfolio- theoretic approach. As pointed out by Smith 1976, many modifications of this option-
pricing model have shown that the analysis is quite robust with respect to relaxation of the basic assumptions under which this model is derived. Recently, many extensions,
Corresponding author. Tel.: 886-2-2621-5656, ext. 2121. E-mail address
: lin9015mail.tku.edu.tw J.-H. Lin 1059-056000 – see front matter
2000 Elsevier Science Inc. All rights reserved.
PII: S1059-05609900043-X
376 J.-H. Lin International Review of Economics and Finance 9 2000 375–386
rather than modifications, of the Black-Scholes valuation model e.g., Johnson Shanno, 1987; Johnson Stulz, 1987; Hull White, 1995; Jarrow Turnbull, 1995;
Klein, 1996 have been presented. Smith also suggests that the Black-Scholes option-pricing model can be used to
value the equity and debt of a firm. A financial intermediary itself is a highly leveraged firm. Merton 1989 and Crouhy and Galai 1991 evaluated financial intermediaries
using a continuous time contingent claim framework. Mullins and Pyle 1994 analyzed risk-based capital rules in a single period model that relied on the Black-Scholes
option valuation. The principal advantage of this valuation technique is the explicit treatment of uncertainty, which has played an important role in discussions of financial
intermediary behavior.
1
Sealey 1980 demonstrated that two divergent approaches, portfolio-theoretic and firm-theoretic, have been employed in the literature to model the financial intermedi-
ary. With the advantage of explicitly treating the uncertainty of the underlying entity, the portfolio-theoretic approach assumes that both loan and deposit markets are
perfectly competitive. Slovin and Sushka 1983 argue that many studies assume that the loan market is competitive but sometimes the loan rate does not clear the market,
the lending operation is constrained by the supply function, and financial intermediar- ies engage in nonprice rationing of loan-borrowers. Slovin and Sushka 1983, Hancock
1986, and Zarruk and Madura 1992 recognized the context of a model of financial intermediary behavior, which assumes that the loan market is imperfectly competitive.
A financial intermediary generally absorbs deposits from a limited geographical area, named a local deposit market, where the area contains only a limited number
of financial intermediaries. Sealey indicates that the deposit rate-setting behavioral mode is the most interesting issue for a financial intermediary. Following Sealey 1980
and VanHoose 1988, the model assumes that the intermediary is a rate-setter, rather than a rate-taker, in a local deposit market to capture the nature of imperfect
competition. The rate-setting behavior incorporated in loan and deposit decisions is the so-called firm-theoretic approach to financial intermediaries.
By applying Dixit and Pindyck 1995, recognizing that lending treated as an invest- ment opportunity is like a financial call option, clarifies the role of uncertainty. The
purpose of this paper is to integrate portfolio-theoretic volatilities with the firm- theoretic rate-setting modes in the analysis of the contingent claim of an imperfectly
competitive financial intermediary.
2
In general, an intermediary is willing to take on more risk to trade a higher rate of return. One of our main findings is that the
relationship between the portfolio-theoretic combined volatilities and the firm-theo- retic rate-setting modes under the Black-Scholes valuation is indeterminate. Further-
more, the effect of changes in the open market security rates returns of default-free asset on the loan rate and deposit rate settings depend on three critical factors: the
borrower-intermediary-lender relationship, portfolio risk, and management of rate- setting strategy. In other words, the redistribution of portfolio compositions and the
strategy for absorbing deposits cannot be optimally determined without examining the firm-theoretic characteristics of the intermediary in the contingent claim analysis.
A possible examination of these indeterminate results may originate from the assump-
J.-H. Lin International Review of Economics and Finance 9 2000 375–386 377
tion of the behavioral modes of imperfectly competitive loan and deposit markets. Therefore, by bridging important linkages between the portfolio-theoretic approach
and the firm-theoretic approach, the contingent claim analysis of a rate-setting interme- diary may be further investigated in this article.
The rest of this article is organized as follows. Section 2 presents a simple model. Section 3 is devoted to the analysis of equilibrium and comparative statics, including
