Here I use log-normal PDF, for it is the most probable function of the three.

Specifically, I assumed that ln(P) follows N[m,s] distribution, and set mean m as ln(100)-s

^{2}/2. That means expected value of P (=E[P]) is always set as 100.

**standard deviation simulation**

First, change standard deviation s from 0.1 to 1.1 by 0.05. Self financing ratio k is set as 1/7 as in the Geithner plan.

X-axis is the simulation factor s, as described above.

P

_{1}is the expected price conditional that non-recourse loan not be used.

P

_{2}is the expected price conditional that non-recourse loan be used.

P

_{b}is the break-even bid price.

p

_{1}(right-hand scale) is the probabaility that non-recourse loan not be used.

As s increases, P

_{1}and P

_{b}goes up, and P

_{2}decreases gradually.

p

_{1}decrease from over 0.9 to near 0.1 for the simulated range of s.

The graph below shows taxpayer's loss (FDIC's loss, to be exact) as percentage of (1-k)P

_{b}(=the value of FIDC non-recourse loan), instead of p

_{1}for the same simulation (right-hand scale). X-axis is same as above, but numbers are changed from s to s/m (coefficient of variance) so that the meaning of x-axis becomes more easy to grasp.

For coefficient of variance of 0.27, FDIC's loss ratio reaches near 60%.

**non-recourse loan ratio simulation**

Next, change self financing ratio k(=1 - non-recourse loan ratio) from 0.05 to 0.95 by 0.05 (this includes Treasury funding). s(standard deviation) is set as 0.5.

(Again, p

_{1}is right-hand scale.)

When k increases from 0.15 to 0.45, P

_{b}premium to E[P] decreases from 22.0% to 2.3%. Maybe low k value(1/7=14.3%) in the Geithner plan was set in order to provide enough (over 20%) subsidy to the bank.

FDIC's loss ratio is as follows.

(Again, loss ratio is right-hand scale.)

If non-recourse loan ratio (1-k) is about 75% instead of 85.7% in the Geithner plan, the loss drops in half (around 20% to 10%). If (1-k) is 50%, loss becomes less than 3%.

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