This preview shows pages 1–2. Sign up to view the full content.
Introduction to derivatives, Fall 2011
BUSI 588, Case 11 solutions
Solutions to Botvinnik  pricing risky debt
1.
(*)
The payoﬀs to Botvinnik are
min(
F,A
T
) =
F
+ min(0
,A
T

F
) =
F

max(0
,F

A
T
)
where
F
is the face value Botvinnik asks for and
A
T
is the value of Tar Heels Chess Corp at
maturity. Figure 1 plots the payoﬀs to Whatsup V Bank.
If Tar Heels Chess Corp undertakes SI (but not KI), then Botvinnik would be receiving the
payoﬀ of a riskfree bond (
F
) minus the payoﬀ of a put option on the values of the assets of
the ﬁrm with strike price
F
. The value of this portfolio of assets is
F
1
.
05
5

P
(
A
= 134
,F,r
f
= 0
.
05
,T
= 5
,σ
= 0
.
5)
where
P
(
·
) denotes the put price according to BlackScholes.
The face value that makes the debt claim (riskfree minus put) equal to the $30m they invest
into the ﬁrm (i.e. the amount that makes them just indiﬀerent betweent investing or not
investing) is
F
= 42
.
7. The implied interest rate they charge is 7
.
3%, i.e. (42
.
7
/
30)
1
/
5

1.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '10
 Staff
 Derivatives, Pricing, Debt

Click to edit the document details