Credit enhancement and loan default risk premiums

Notes

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.