# On the economics of financial guarantees

In the Credit Risk lecture note and in Problem Set 9, we study how credit enhancement of risky debt works. Examples of credit enhancement in the real world include federal deposit insurance, federally guaranteed student loans, public and private bond insurance, pension insurance, mortgage insurance, government loan guarantees, etc.; the list goes on.

Most credit enhancement schemes work in the following fashion. Creditors loan money to “risky” borrowers who own risky assets worth \$V(F) today (at date t = 0).  Borrowers are risky in the sense that at date T, they will default (in whole or in part) if \$F < \$B.  The shortfall suffered by creditors resembles a put option with date T payoff of –Max[0, BF]. Therefore, without credit enhancement, the value of risky debt today (at t = 0) is

$V(D) = B{e^{ - rT}} - V(Max[0,B - F]).$

However, when credit risk is intermediated by a guarantor (e.g., an insurance company or government agency), credit risk is transferred to the guarantor who receives an upfront “premium” worth $V(Max[0,B - F])$ at t=0 in exchange for having to cover a shortfall of $Max[0,B - F]$ which may occur at date T. If all credit risk is transferred to the guarantor, then from the creditors’ perspective it is as if the borrowers have issued riskless debt. Therefore, creditors charge borrowers the riskless rate of interest and receive the promised payback from two sources: 1) borrowers pay $D = B - Max[0,B - F]$, and 2) the guarantor pays $Max[0,B - F]$.  Therefore, creditors get paid back $B - Max[0,B - F] + Max[0,B - F] = B$.