The Geithner put : option formula

In the previous post , I showed the general formula of break-even purchase price under Geithner plan.

In that post, I showed the gain/loss of the investment fund as follows:
　　　w(P - P_b)　　　if P >= (1-k)P_b
　　　-wP_b　　　　　 if P < (1-k)P_b
where:
P is true price of the loan,
P_b is the purchase price,
(1-k) is ratio of non-recourse loan offered by FDIC (6/7 in case of Geithner plan),
w is ratio of fund money in investment (1/2 in case of Geithner plan; the rest(=1-w) is funded by Treasury).

It also can expressed in option formula as follows:
　　　w{Max(P-P_b , -kP_b)}
　　=w{Max(P-(1-k)P_b , 0)-kP_b}

This is the formula of call option with strike price=-(1-k)P_b and option purchase price=kP_b (See image below).


By applying the above option formula, it can be calculates as
　　　0.5*{(0.5*(100-84*6/7)+0.5*0)-84/7}=1
which corresponds to Nemos's result.

As Nemo showed, the money fund put in is wkP_b=0.5*1/7*84=6. So the fund performance reaches 1/6*100=16.67%.

FDIC gain/loss also can be expressed in option formula as follows:
　　　-Max(0 , (1-k)P_b-P)
(In fact, maximum gain is not zero, as there is interest revenue. Here I ignore it for simplicity)

This is the formula of put option with strike price=-(1-k)P_b (See image below).


The FDIC position is short on this put option, and that "Geithner put" is what enables the floor part of the fund's call option shown above.