Delay and Haircuts in Sovereign Debt - University of St Andrews

value for the Optimistic debtor is
( + s)
+ (1 ) ~x 2 + (1 ) +
:
2 2
2 2
After a simpli…cation, we …nd that the Optimistic debtor’s continuation
value is given by .
(+s)
4
The continuation value for the Cautious debtor is
t = 2, the Cautious debtor o¤ers (x 0 2 ;
x0 2
(+s)
2
since, at
) with a probability 1 and the
creditor rejects the debtor’s o¤er of (x 0 2 ; x0 2 ) with a probability 1.
Finally, the continuation value for the creditor is given by
q 0 x 0 2
+ (1 ) ( ~x 2 ) (
+ (1 q 0 )
2
s)
;
where the …rst term refers to the creditor’s payo¤ if the debtor is Optimistic
and the second term refers to the creditor’s payo¤ if the debtor is Cautious.
After a simpli…cation and a substitution of the term ~x 2 , we obtain:
(
2
s)
1
s
(1 q 0 ) +
s
Scenario 2: The debtor does not know her own type
s
s
(1 q 0 ) x 0 2 :
Under this scenario, the creditor’s continuation value is the same as in
Scenario 1, but the debtor’s continuation payo¤ is
q 0 x 0 2 + (1 ) ~x 2 +
+ (1 q 0 )
2
2
which after substitution and simpli…cation becomes
2 ( + s)
2
2
q0
:
2
( + s)
2
;
In the …rst period, the sovereign debtor is a proposer. It follows from the
two scenarios we considered above that the expected payo¤ for the creditor
from rejecting the debtor’s o¤er at t = 1, ^a, is given by
0 h
p q 0 ( ( L x 0 2
^a = @
) + (1 ) ( L ~x 2 )) + (1 q 0 )
h
+ (1 p) q 0 ( ( H x 0 2 ) + (1 ) ( H ~x 2 )) + (1 q 0 )
i
(L s)
2
(H
2
s)
i
1
A :
32