Method and system for determining a company's probability of no default
Using observable market factors which reflect a current share price, a given share price, volatility in given share price, expected debt recovery fraction, and percentage standard deviation in the expected debt recovery fraction, the instant invention provides probability estimates for no default by a company within a given future time horizon. The invention has applications in the field of bond and company rating and calculation of credit spreads. The invention also provides a relationship between credit spreads, equity prices and volatility, useful as a price discovery tool in determining fair market price of the credit risk, on a name basis for credits that have public equity.
1. A method at least partially implemented in a computer for determining a company's probability of no default over a time period between t=0 and t=T comprising:
determining a standard deviation σ* s of past share prices in the company;
determining a current share price S 0 of the shares in the company
determining a given share price S* of the shares in the company;
determining a debt per share D of the shares in the company;
determining a expected debt recovery fraction {overscore (L)};
determining a percentage deviation λ in the expected debt recovery fraction {overscore (L)}; and
determining and displaying B(T) as the company's probability of no default between t=0 and t=T using at least σ* s, S 0 , S*, D, {overscore (L)} and λ with equations mathematically equivalent to:
d
=
(
S
0
+
L
_
D
)
exp
(
λ
2
)
L
_
D
;
A
T
2
=
(
σ
s
*
S
*
/
(
S
*
+
L
_
D
)
)
2
T
+
λ
2
;
and
B
(
T
)
=
N
[
ln
(
d
)
A
T
-
0.5
A
T
]
-
d
*
N
[
-
ln
(
d
)
A
T
-
0.5
A
T
]
,
wherein N is a cumulative normal distribution function.
2. A method according to claim 1 , further comprising: determining a default spread s(t) for a time t=T using at least an equation mathematically equivalent to:
s
(
T
)
=
-
(
1
T
)
ln
(
B
(
T
)
)
.
3. A method according to claim 1 , further comprising: determining a normalized probability of no default Z(t) for a time t=T, wherein B(T) is B(t) evaluated at time t=T, and B(0) is B(t) evaluated at time t=0, using at least an equation mathematically equivalent to:
Z
(
T
)
=
B
(
T
)
B
(
0
)
.