'I
•
•
•
Price Volatility
is a Function
of
Duration
and Convexity
The larger the Duration,
the more volatility
in prices
from
changes
in yields.
Duration always stated
as a positive number.
Convexity
matters
most when
change in yield is big.
M 1
2

""D!:"y+CM(!:"y)
P
2
Approximating
Duration
and Convexity
•
Approximate
Duration
'"
P P+
2(P
o
)(Lly)
•
Approximate
Convexity",
P++P_ 2P
o
P"(Lly)'
Valuation
of Defaultable
Bonds
vow take a bond with face value F and samtannuarccupcn
payments
equal to C maturing
T semiannual
periods
ahead.
Suppose:
_ there is
d
probability of default at any given payment date.
_ in case of default
bondholders
receive a recovery
value
R<F
at the time of default, instead of the remaining promised
cashflows.
Ifthe discount rate (expected
return) for the bond's cash flows is
r
per semiannual
period, what is the fair price of the bond?
 3
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View Full DocumentExpected
Loss
Expected
loss
=
F  ((ld)*F
+
d*R)
=
F*(l(ld»)
d*R
=
d*F  d*R
=
d*(F 
R)
Expected
Loss
=
(Probability
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 Fall '11
 Hood
 Volatility, Credit rating, default bondholders, credit risk characteristics, lower rated entities

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