Academic journal article Journal of Money, Credit & Banking

Correlated Default Risks and Bank Regulations

Academic journal article Journal of Money, Credit & Banking

Correlated Default Risks and Bank Regulations

Article excerpt

MODELING BANK RISK is an issue of keen regulatory importance. If solvency regulations (such as deposit insurance and capital standards) do not fully adjust for the bank's asset risk, the bank would have a moral hazard incentive to increase asset risk to increase the regulator's (and ultimately the taxpayer's) loss burden.

The bank's asset portfolio is generally viewed in an "aggregated" sense in the extant literature. For instance, in a seminal paper Merton (1977) noted that the deposit insurance liability could be viewed as a put option on the bank's aggregate portfolio value with a strike price equal to the face value of the bank's deposit debt. In order to estimate the value of the deposit insurance put analytically, Merton (1977) assumed that the bank's aggregate value followed a Geometric Brownian Motion (GBM). Following Merton (1977), numerous papers have considered more refined option-theoretic approaches to pricing deposit insurance. (1) However, the majority of these papers begin with a fundamental assumption, viz., the bank's aggregate asset portfolio value obeys an assumed stochastic process. Such an "aggregated" approach "almost totally suppresses the question of bank portfolio composition" (Flannery 1989). That is, the traditional approach ignores the fact that a bank's portfolio is made up of loans to individual (corporate) borrowers with different levels of asset risk and leverage.

Two notable exceptions in this regard are papers by Dermine and Lajeri (2001) [henceforth DL] and Flannery (1989). DL consider the borrower's asset dynamics as the primitive risk in the economy, and highlight the truncated nature of a loan's payoff on deposit insurance premia. However, DL only consider the case of a single borrower. As a result, in DL's framework, as in the standard (Merton 1977) option-theoretic context, bank shareholders are indifferent among various loan compositions so long as the portfolio attains a specific level of overall portfolio risk. In contrast, Flannery (1989) considers "the properties of individual assets (loans) within the (bank) portfolio." Flannery's analysis highlights the ambiguous impact that increased individual loan risks has on the value of a bank's deposit insurance coverage. (2) However, unlike DL, Flannery (1989) does not analyze the truncated nature of loan payoffs and the manner in which the borrower's asset volatility and leverage could affect the individual loan's risk.

Our paper may be viewed as complementary to these studies. Like Flannery (1989) we too consider the bank's portfolio as comprising of several individual loans. Moreover, like DL, we model the individual borrower's asset volatilities as the primitive risks in the system and explicitly consider the truncated payoff on bank loans. Thus, as in DL, loan risk stems from the underlying borrower's volatility and leverage in our "dis-aggregated" framework. However, unlike the extant literature, our model explicitly incorporates the effects of diversification and correlated individual loan default risks on the bank's aggregate payoff distribution.

Although such a "dis-aggregated" perspective of the bank's loan portfolio is conceptually more accurate, its practical relevance may appear to be limited at first glance. If the aggregate bank payoff (value) at maturity is approximately lognormal, the distinction between the traditional and the dis-aggregated views of the bank portfolio would be moot for practical purposes. We empirically examine the magnitude of the approximation error inherent in the aggregate approach by modeling a bank's portfolio as a portfolio of loans to a number of corporate borrowers, and assuming that the asset values of these individual corporate borrowers, rather than the aggregate value of the bank's portfolio, are lognormally distributed.

Our "dis-aggregated" model highlights two aspects of the bank portfolio. First, individual loan's terminal payoffs are not lognormally distributed since loan contracts have truncated payoffs. …

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