Optimal Guarantee Control

Didier Cossin
Institute of Banking and Financial Management, University of Lausanne
Didier.Cossin@hec.unil.ch

Abstract

Consider any type of guarantee (and indeed there are many types of them, as described later). Suppose that the value of one such guarantee depends on some assets, or some combination of assets and liabilities. Suppose also that the guarantor can monitor these assets, possibly with cost, and control them with cost (for example, seize them under some circumstances or restrict their use, or ask for new collateral). The goal of this research is to design a program that will provide such a guarantor with the optimal timing for its monitoring of assets as well as the optimal timing and the optimal size, strength, or breadth of its controls. Such a program provides a set of prescriptions for determining when to monitor the assets securing a guarantee, when to ask for changes in the behavior of these assets, and how to gauge the level of change to request. The program thus described goes beyond the well analysed valuation of guarantees and provides a methodology for optimal control of guarantees.

In this analysis, the term ``guarantee" pertains to a wide range of applications of the analysis. Guarantees pervade financial contracts, both explicitly and implicitly and an optimal guarangee control program can be used in a variety of situations.

Essentially a guarantee is a bonding contract whereby the guarantor commits itself to fulfill a financial contract if the guaranteed party fails to do so. Foremost among explicit private guarantees are guarantees of the debt obligations of subsidiaries from parent corporations; letter-of-credit guarantees, provided by commercial banks; swap guarantees; mortgage guarantees; insurance contracts of all sorts.

Implicit private guarantees are even more widely used. Any risky loan can be considered a combination of a riskless contract and a guarantee, as shown by Merton and Bodie (1992). In essence the following optimization program will be valid for the control of such loans, especially collateralized loans when the collateral can be monitored and controlled. Further, the program will be valid for the control of any financial contract at risk of default (swaps, CMOs, etc.), because any risky contract, like a risky loan, can be decomposed in a safe contract and a guarantee. Note also that the provider of the guarantee need not be a third party. Although the guarantee can and should be distinguished both in function and in value from the riskless part of the contract, when implicit guarantees are considered, the provider of the guarantee is also a parti to the contract. Therefore two entities are active, versus three in the context of explicit guarantees. Thus the models presented later pertain as much to the control of credit risk as to the control of ``guarantees" in the traditional sense of the term.

Public guarantees are also widespread. Government guarantees of loans made to private corporations have made headlines on each side of the Atlantic. The $1.5 billion US guarantee of Chrysler Corporation in 1980 and the £200 million UK guarantee of International Computers Limited (ICL) in 1981 are just two prominent examples. Government-issued small business guarantees as well as export-oriented and industry-targeted guarantees represent current government practices for financing economic activity. Even more essential may be the role of guarantees of deposits through the Federal Deposit Insurance Corporation (FDIC) and less extensive, but similar, guarantees of pension benefits (through the Pension Benefit Guaranty Corporation of PBGC), students loans (through the Student Loan Marketing Association of Sallie Mae), residential mortgages (through the Federal National Mortgage Association or Fannie Mae, and the Federal Home Loan Mortgage Corporation or Freddie Mac), etc.

To elaborate on the widespread use of guarantees in both private and public finance today, Appendix 1 presents a survey of situations in which guarantees explicitly of implicitly play a major role (See also Hirtle (1987)). this survey supports two premises: (1) guarantees are a pervasive financial instrument, and (2) optimal control of guarantees can be an important competitive advantage for some companies - even a necessity then competition is severe - and, in the case of public finance, it can result in significant savings for taxpayers.

The use of guarantees is likely to become even more widespread in the future. The enormous amount of recent financial innovation highlights the importance of contract fault and of credit sensitivity, as evident, for example, in swap trading. As noted earlier, any form of default signals the existence of an implicit guarantee needing to be controlled. The need for specific applications of the type of programs presented here is likely to grow with the use of explicit or implicit guarantees in new financial contracts.

This study provides a method for optimal timing of the monitoring and control of assets' behavior. Current general practice relies on standard rules of thumb to monitor assets, tracking them through annual or quarterly audits (or daily, for example, in margin accounts). Seizure or control policies of assets securing guarantees have been based on static capital ratios, with some discretionary power often used by the guarantor to skirt these rules.

It is key to note that the profitability of offering guarantees depends on optimal monitoring and optimal control. Management of guarantees extends beyond containing operating costs. Even adequate premiums based on historic value of the assets (even those calculated using refined theories such as contingent-claim analysis) are not enough to ensure profit maximization. First, fair premiums are valid only under the condition that neither the guaranteed party nor the guarantor can influence the dynamic path of the values of the assets or liabilities impacting the value of the guarantee without the immediate knowledge of the counterparty. In a realistic agency setting, however, a moral hazard problem arises: The guaranteed party has strong incentives to influence the stochastic process of the underlying assets' prices. (See Section 4.A) Influence strategies may include hiding the true level of assets' value or increasing their variance to increase the value of the corresponding put option. If, as appears realistic, the guarantor cannot monitor the assets continuously, then risk-based premiums will be insufficient to ensure that the guarantor's cost is in line with the requested premium.

Second, for regulatory or marketing reasons, it is often difficult to implement risk-based premiums. In these cases, even with no information asymmetry, a control of the type described here may prove essential. Even when premiums are not absolutely flat over risk, there are many cases in which only a global approximation of risk or a discrete approximation (such as use of risk categories in insurance) is used to calculate the premium. In these cases, where so-called risk based premiums represent only a discrete approximation to the real ones, optimal control will also be important.

This paper analyzes two sets of programs for optimal guarantee control. The programs characterize the minimal cost of guarantees and the optimal behavior leading to the minimal cost. One set of programs applies to cases in which information is readily accessible, the other applies to cases in which costly audits must determine the value of the assets. The programs can help guarantors review the cost effectiveness of their current auditing and control practices, especially in terms of the resulting level of protection against the risks of shortfall.

The paper is organized as follows. We start by reviewing the main axes of literature that frame this paper (Section I.) The following sections present the model and its setting, with the analysis of the full observation case, both for repeated control (Section II) and optimal seizure (Section III). The program for the partial observation case follows, first for repeated control (Section VI), then for optimal seizure (Section V). The numerical analysis of a simple situation is then given as illustration (Section VI). Conclusions (Section VII) precede illustrative figures, a first appendix presenting a wide array of examples of guarantees and a second one summarizing the models notation.