Credit enhancement and loan default risk premiums

Credit enhancement and loan default risk premiums

Chuang-Chang Chang


Using contingent claims analysis, we study the impact of private guarantees on the default risk premiums or credit spreads of discount loans. Specifically, we analyze the reduction of the default risk premium on a new junior loan by obtaining the numerical estimates under a stochastic interest rate. We demonstrate how the value of credit enhancement relates to the profitability and size of the new junior loan, as well as the leverage, asset risk, and debt seniority of the borrowing firm and the private insurer The main results show that (a) for the new junior loan, although the benefits of financial insurance are substantial with an AAA-rated private insurer, in general, default risk premiums can only be reduced to a minute amount; and (b) even with complete insurance coverage from an AAA-rated private insurer loan issues command default risk premiums that reflect not only the intrinsic values and risks of the insured and the insurer but also their covariance.

A financial guarantee is a commitment by a third party to make payment in the event of default by a borrower in a credit or a loan agreement. Widespread thirdparty guarantees, public or private, include default insurance on corporate loans, municipal bonds, whole mortgages, and mortgage pools.1 Insurance companies and commercial banks as well as public agencies offer guarantees to a number of financial instruments such as letters of credit, loans, deposits, swaps, mortgages and municipal bonds insurance (e.g., Greenwald, 1998; Lonkevich, 2000; Merton & Bodie, 1992;). Guarantees can be implicit or explicit; for instance, subsidiaries often benefit from implicit guarantees by their parent companies with respect to their financial obligation, hence reducing their cost of capital.

Financial guarantees also play a major role in the development of international commerce. Financial guarantees improve access to international capital markets at lower costs, longer maturities and for larger amounts (e.g., Euromoney, Dec. 1997/Jan. 1998; World Bank, 1995). Furthermore, exporting firms often benefit from governmental or private insurance guarantees to assist them in expanding their activities overseas. For instance, the Insurance Bureau of Canada reports the increasing role a public agency, Export Development Canada, plays in the exported-related and credit insurance market (Journal de l’Assurance, 1999). Multilateral development banks, such as the World Bank, currently endorse several private investment projects in emerging countries (World Bank, 1995).

Financial guarantees have become a major tool for risk management and financial innovation facilitating credit enhancement and hedging. Recent financial crises in Asia and Eastern Europe underscore the importance of appropriate immunization against default risk (e.g., Euromoney, Dec. 1997/Jan. 1998).

In a financial-engineering perspective, Merton and Bodie (1992) show that the purchase of any loan is equivalent in both a functional and a valuation sense to the purchase of a pure default-free loan and the simultaneous issue of a guarantee for that loan. Merton and Bodie (1992) also show why guarantees are pervasive and why the analysis of guarantees has relevance to the evaluation of virtually all financial contracts, whether or not the guarantees are explicit. Ceteris paribus, in the absence of external guarantees, a corporate debt trades in the market at rates reflective of its private default risk.

With the exception of Lai (1992) and Lai and Gendron (1994), all studies which use contingent claims analysis focus on the valuation of loan guarantees by the federal government and its sister agencies, which may be considered default-free (as buttressed by the works of Merton, 1977; Jones & Mason, 1980; Sosin, 1980; Chen, Chen, & Sears, 1986; Selby, Franks, & Karki, 1988; and Duan & Yu, 1994, 1999). Lai (1992) presents a model of private loan guarantees when the insurer is subject to default risk, but does not examine either Merton’s (1974) default risk premium, defined as the spread between the yield on the loan and the riskless rate, nor the reduction of default risk provided by third-party credit enhancement.

In the spirit of Merton’s (1974) analysis of pure discount bonds2 and that in Chen et al. (1986), Doherty and Garven (1986), and Lai (1992), we use the risk-neutral valuation framework of Rubinstein (1976), Brennan (1979), and Stapleton and Subrahmanyam (1984). Without imposing a no-loss no-gain condition on the debtholders as does Sosin (1980), we analyze theoretically the impact of loan guarantees in terms of the reduction of the default risk premium on the new junior loan guaranteed by a private insurer. As no closed-form formula (1973) can be obtained, we perform a Monte Carlo simulation to derive comparative statics for the loan default risk premium of the new junior loan with and without a private credit enhancement under stochastic interest rates. As such, we combine the literature of the modeling of credit spreads with the one on financial guarantee insurance to study the impact of credit enhancement on the default risk of discount loans. Such a study has not appeared in the extant literature. Our simulation results indicate that there is a substantial reduction of the default risk premium of the new junior loan brought about by the private guarantee.

Unlike the absolute case of a government guarantor with full faith and credit, which eliminates entirely the default risk premium of the junior debt, the private full guarantee can only reduce the default risk to a minute amount. Even with credit enhancement, both the firm’s default risk, and to a certain extent the guarantor risk, and creditworthiness are priced in the loan. In effect, we provide a theoretical explanation for Hsueh and Chandy’s (1989) empirical finding that the debt issuer’s default risk continues to affect the debt yield even with the added high-rated credit insurance.

Our paper continues in three sections. The next section describes the theoretical framework used to derive the default risk premia of the debts. The third section presents and discusses the numerical results. The final section draws conclusions.

A Model of Loan Default Risk Premia With Private Guarantees

We follow the Rubinstein (1976), Brennan (1979), and Stapleton and Subrahmanyam (1984) framework of a risk-neutral valuation relationship (RNVR) for contingent claims pricing in a discrete-time setting. This valuation technique is appropriate when continuous trading and a continuously hedged riskless portfolio are not possible or do not exist. In our setting, both the contingent claims (e.g., third-party guarantees) and the underlying assets they support (i.e., loans) are not freely traded. We ignore all potential agency problems inherent in financial contracting and we assume no violation of the absolute priority rules (APR).3 We recognize that differences in the assumption concerning default and the amount recovered in bankruptcy greatly affect the valuation of debt (see for instance, Hull & White, 1995; Longstaff & Schwartz, 1995; Leland & Toft, 1996).4

To simplify the analysis, under standard assumptions (perfect markets, symmetric information, etc.), we assume a single-period model and allow the interest rate to be stochastic. There are also no payouts from either the firm or its guarantor to shareholders and bondholders before the maturity date of the discount debt.

Following Merton (1974), Gorton and Santomero (1990) and others, we define the default risk premium (DRP) as the spread between the yield on the debt and the risk free rate of the same duration. For all approaches, we first calculate the default risk premium of the new junior loan without a guarantee. We then compute the default risk premium of the new junior loan with a guarantee. Finally, we estimate the reduction in the loan risk premium brought about by credit enhancement by differencing these two default risk premiums.


Using the framework of Merton (1974) and Chen et al. (1986), we extend the works of Merton (1977), Jones and Mason (1980) and others to derive the reduction of the default risk premia of pure discount debts resulting from a private and risky credit enhancement. For the new junior loan, unlike the case of full faith and credit from a government guarantee, although the benefits of financial insurance are substantial, we find in general that default risk premia cannot be eliminated entirely by private insurance. In particular, we provide a theoretical explanation for why the interest rates on intrinsically regular AAA-rated municipal bonds have persistently been below those of insured bonds even though the “received” (or labeled, via the credit rating from credit agencies) of the insured debt is equivalent to that of regular AAA bonds issues in the market (see Hsueh & Chandy, 1989). Empirical evidence which shows that the value of the deposit insurer’s credit enhancement varies with its own level of solvency (e.g., Cook & Spellman, 1991, 1996) is also consistent with the results of our model. Furthermore, even with complete insurance coverage from an AAA-rated private insurer, loan issues command default risk premia that reflect not only the intrinsic values and risks of the insured and the insurer, but also their covariance.


1 The interest rate-cost net benefits of private bond insurance have been settled empirically. See among others, Quigley and Rubinfeld (1991), Kidwell, Sorensen, and Wachowicz (1987), and Hsueh and Chandy (1989).

2 Note that for a default-free coupon bond, Jamshidian (1989) has shown that the European options on the ncoupon bearing bond are the sum of n options on the underlying discount bond. Sarig and Warga (1989) report that both the federal government and corporations have recently issued increasing numbers of pure discount (zero-coupon) bonds. This increase, motivated by tax considerations, is intended to satisfy investors’ desire to better tailor their investment portfolio to the time pattern of their cashflow needs.

3 There is evidence of the departures of the APR (see for instance Betker, 1995; Eberhart, Moore, & Roenfeldt, 1990; and Weiss, 1990, among others). However, Beranek, Boehmer, and Smith (1996) clarify the APR and explain why departures from it are permitted by the U.S. bankruptcy code in certain circumstances. Their sample of 68 reorganizations revealed no evidence that bankruptcy judges were incorrectly applying legal priority rules.

4 To be viable, a private insurer exerts tight monitoring of

the insured firm to prevent any deviation from the APR. The study of the impact of the APR violation on the valuation of a loan guarantee is left to later studies.

5 As in Sosin (1980), we assume in a competitive loan market that the initial value of the junior debt is equal to the project cost. Alternatively, to focus on credit risk, in a certainty-equivalent framework the loan’s expected face value is assumed to have no systematic risk.

6 For the discrete-time single-period model, the time to maturity is accounted in the period-wide input values for the risk-free rates, the firm, and the guarantor asset risks.

7 With lambda = -0.06 as estimated in Chen and Scott (1992), the results do not change qualitatively. In addition, the volatility implicit in the Chan et al. (1992) parameters is high, relative to what is seen in the market.

8 The mechanics of the Monte Carlo simulations of the three state variables are standard (see for instance, Abken, 1993). The standard deviations of our simulations are less than 0.5% of the default risk premiums.

9 The default risk premium of the new loan approaches zero when we set V equal to 1,000,000. This test confirms that the DRP approaches zero when V approaches infinity. We thank a reviewer for pointing out this characteristic.

10 As pointed out by Black and Cox (1976), since the value of the firm is significantly higher than the promised payment on the senior debt (D), the junior debt has more pronounced debt characteristics and the default risk premium is everywhere an increasing function of the firm’s postproject asset risk.

11 Sarig and Warga (1989) have empirically investigated the risk structure of interest rates using pure discount bonds. A number of authors also studied the risk structure of interest rates on coupon debt. For instance, Cooper and Mello (1988) developed a numerical procedure that generates the default risk premium on fixed and floating rate non-amortizing bonds, while Smith and Zumpano (1993) used a two-state option-pricing model to price the option to default on risky fixed-rate coupon debt. However, none of these authors study the effects of credit enhancement by private and vulnerable insurers on the risk structure of interest rates.

12 It can be easily verified that the long-term interest rate is about 9% at our parameter settings for the CIR interest rate process.


Abken, PA. (1993). Valuation of default-risky interest-rate swaps. Advances in Futures and Options Research, 6, 93116.

Beranek, W., Boehmer, R., & Smith, B. (1996). Much ado about nothing: Absolute priority deviations in Chapter 11. Financial Management, 25 (3), 102-109.

Betker, B. (1995). Management’s incentives, equity’s bargain

ing power, and deviations from absolute priority in Chapter 11 bankruptcies. Journal of Business, 68, 161-183.

Black, F. & Cox. J. (1976). Valuing corporate securities: Some effects of bond indenture provisions. Journal of Finance, 31, 351-367.

Brennan, M. (1979). The pricing of contingent claims in discrete time models. Journal of Finance, 34, 53-68.

Chan, K.C., Karolyi, A.K., Longstaff, F, & Sanders A. (1992). An empirical comparison of alternative models of the short-term rates. Journal of Finance, 47, 1209-1227.

Chen, A.H., Chen, K.C., & Sears, R.S. (1986). The value of loan guarantees. The case of Chrysler Corporation. Research in Finance, 6, 101-117.

Chen, R. & Scott, L. (1992). Pricing interest rate options in a two-factor Cox-Ingersoll-Ross model of term structure. Review of Financial Studies, 5, 613-636.

Cook, D.O. & Spellman, L.J. (1991). Federal financial guarantees and the occasional market pricing of default risk: Evidence from insured deposits. Journal of Banking and Finance, 15, 1113-1130.

Cook, D.O. & Spellman, L.J. (1996). Firm and guarantor risk, risk contagion, and the interfirm spread among insured deposits. Journal of Financial and Quantitative Analysis, 31, 265-281.

Cooper, 1. & Mello, A. (1988). Default spreads in the floating interest rate markets: A contingent claims approach. Advances in Futures and Options Research, 3, 269-289.

Cox, J.C., Ingersoll, J.E., & Ross, S.A. (1985). A theory of term structure of interest rate. Econometrica, 53, 385-407. Doherty, N.A. & Garven, J.R. (1986). Price regulation in prop

erty-liability insurance: A contingent claims approach. Journal of Finance, 41, 1031-1050.

Duan, J.-C. & Yu, M.-T. (1994). Forbearance and pricing deposit insurance in a multiperiod framework. Journal of Risk and Insurance, 61 (4), 575-591.

Duan, J.-C. & Yu, M.-T. (1999). Capital standard, forbearance and deposit insurance coverage under GARCH. Journal of Banking and Finance, 23 (11), 1691-1706.

Eberhart, A., Moore, W.T., & Roenfeldt, R. (1990). Security pricing and deviations from the absolute priority rule in bankruptcy proceedings. Journal of Finance, 45, 14571469.

Euromoney. (1997, Dec/ 1998, Jan). A special report by Asian Securitization and Infrastructure Assurance (Pte) Ltd. Euromoney Publications PLC.

Gorton, G. & Santomero, A. (1990). Market discipline and bank subordinated debt. Journal of Money, Credit, and Banking, 22, 119-128.

Greenwald, J. (1998). Financial guarantee insurers diversify to grow business. Business Insurance, 32, 1-61.

Hull, J. & White, A. (1995). The impact of default risk on the prices of options and other derivative securities. Journal of Banking and Finance, 19, 299-322.

Hsueh, P. & Chandy, PR. (1989). An examination of the yield spread between insured and uninsured debt. Journal of Financial Research, 12, 235-244.

Jamshidian, F. (1989). An exact bond option pricing formula. Journal of Finance, 44, 205-209.

Jones, E.P. & Mason, S.P. (1980). The valuation of loan guarantees. Journal of Banking and Finance, 4, 89107.

Journal de l’Assurance. (1999, Jan). Les assureurs lARD veulent briser la mainmise de It-tat en assurance cr6dit A 1’exportation, 16-17.

Kidwell, D., Sorensen, E., & Wachowicz, J. (1987, September). Estimating the signaling benefits of debt insurance: The case of municipal bonds. Journal of Financial and Quantitative Analysis, 22, 299-313.

Lai, V.S. (1992). An analysis of private loan guarantees. Journal of Financial Services Research, 6, 223-248.

Lai, V.S. & Gendron, M. (1994). On financial guarantee insurance under stochastic interest rates. Geneva Papers on Risk and Insurance Theory, 19, 119-137.

Leland, H. & Toft, K. (1996). Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads. Journal of Finance, 51, 987-1019.

Longstaff, F. & Schwartz, E. (1995). A simple approach to valuing risky fixed and floating rate debt. Journal of Finance, 50, 789-819.

Lonkevich, D. (2000). Joint ventures boost financial guaranty market. National Underwriter, 100, 16-17.

Merton, R.C. (1974). On the Pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29. 449470.

Merton, R.C. (1977). An analytic derivation of the cost of deposit insurance and loan guarantees: An application of modern option pricing theory. Journal of Banking and Finance, 1, 3-11.

Merton, R.C. & Bodie, Z. (1992). On the management of financial guarantees. Financial Management, 21, 87-109. Quigley, J.M. & Rubinfeld, D.L. (1991). Private guarantees for

municipal bonds: Evidence from the aftermarket. National Tax Journal, 44, 29-39.

Rubinstein, M. (1976). The valuation of uncertain income streams and the pricing of options, Bell Journal of Economics, 7, 407-425.

Sarig, 0. & Warga, A. (1989). Some empirical estimates of the risk structure of interest rates., Journal of Finance, 44, 1351-1360.

Selby, M.J.P., Franks, J.R., & Karki, J.P. (1988). Loan guarantees, wealth transfers and incentives to invest. Journal of Industrial Economics, 37, 47-65.

Smith, W.S. & Zumpano, L.V. (1993). The default risk structure of interest rate: The case of coupon debt. Advances in Futures and Options Research, 6, 193-215.

Sosin, H.B. (1980). On the valuation of federal loan guarantees to corporations. Journal of Finance, 35, 1209-1221. Stapleton, R. & Subrahmanyam, M. (1984). The valuation of

multivariate contingent claims in discrete time models. Journal of Finance, 39, 207-228.

Weiss, L. (1990). Bankruptcy resolution: Direct costs and violation of priority of claims. Journal of Financial Economics, 2, 285-314.

The World Bank. (1995, September). The World Bank guarantee: Catalyst for private capital flows. Washington, DC: The World Bank Group.

Chuang-Chang Chang

National Central University, Taiwan

Van Son Lai

Laval University

Min-Teh Yu

Providence University, Taiwan

Address all correspondence to Van Son Lai, Department of Finance and Insurance, Faculty of Administrative Sciences, Laval University, Quebec, QC, Canada GIK 7P4. E-mail: The authors thank Chung-Gee Lin and Shih-Cheng Lee for research assistance and acknowledge the financial support provided by the NSC of Taiwan. Lai acknowledges financial support from the Social Sciences and Humanities Research Council of Canada.

Copyright Administrative Sciences Association of Canada Sep 2002

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