US2008262884A1PendingUtilityA1
Methods for determining value at risk
Individually held — no corporate assignee on recordPriority: May 1, 2000Filed: Apr 8, 2008Published: Oct 23, 2008
Est. expiryMay 1, 2020(expired)· nominal 20-yr term from priority
Inventors:Ulrich Müller
G06Q 40/03G06Q 40/00G06Q 20/102G06Q 40/04G06Q 20/10G06Q 40/08
63
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0
Cited by
0
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0
Claims
Abstract
A preferred embodiment comprises a method for determining value-at-risk based on tick-by-tick financial data. Major steps of the method comprise the following: (1) financial market transaction data is electronically received by a computer; (2) the received financial market transaction data is electronically; (3) a time series z is constructed that models the received financial market transaction data; (4) an exponential moving average operator is constructed; (5) an operator is constructed that is based on the exponential moving average operator; (6) a causal operator Ω[z] is constructed that is based on the iterated exponential moving average operator; (7) values of predictive factors are calculated; (8) the values calculated by the computer are stored in a computer readable medium, and (9) value-at-risk is calculated from the values stored in step (8).
Claims
exact text as granted — not AI-modified1 . A method of determining value-at-risk, comprising the steps of:
constructing an inhomogeneous time series z that represents received financial market transaction data; constructing an exponential moving average operator EMA[τ, z]; constructing an iterated exponential moving average operator based on said exponential moving average operator; constructing a time-translation-invariant, causal operator Ω[z] that is a convolution operator with kernel ω and that is based on said iterated exponential moving average operator; electronically calculating values of one or more predictive factors relating to said time series z, wherein said one or more predictive factors are defined in terms of said operator Ω[z]; and electronically calculating value-at-risk from said calculated values of one or more predictive factors.
2 . The method of claim 1 , wherein said operator Ω[z] has the form:
Ω
[
z
]
(
t
)
=
∫
∞
t
′
ω
(
t
-
t
′
)
z
(
t
′
)
=
∫
0
∞
t
′
ω
(
t
′
)
z
(
t
-
t
′
)
.
3 . The method of claim 1 , wherein said exponential moving average operator EMA[τ; z] has the form:
EMA
[
τ
;
z
]
(
t
n
)
=
μ
EMA
[
τ
;
z
]
(
t
n
-
1
)
+
(
v
-
μ
)
z
n
-
1
+
(
1
-
v
)
z
n
,
[
[
with
α
=
τ
t
n
-
t
n
-
1
]
]
where
α
=
t
n
-
t
n
-
1
τ
μ
=
-
α
,
and
v is a value that depends on a chosen interpolation procedure.
4 . The method of claim 1 , wherein said operator Ω[z] is a differential operator Δ[τ] that has the form:
Δ[τ]=γ(EMA[ατ, 1]+EMA[ατ, 2]−2 EMA[αβτ, 4]), where γ is fixed so that the integral of the kernel of the differential operator from the origin to the first zero is 1; α is fixed by a normalization condition that requires Δ[τ; c]=0 for a constant c; and β is chosen in order to get a short tail for the kernel of the differential operator Δ[τ].
5 . The method of claim 4 wherein said one or more predictive factors comprises a return of the form r[τ]=Δ[τ; x], where x represents a logarithmic price.
6 . The method of claim 1 wherein said one or more predictive factors comprises a momentum of the form x-EMA[τ; x], where x represents a logarithmic price.
7 . The method of claim 1 wherein said one or more predictive factors comprises a volatility.
8 . The method of claim 7 wherein said volatility is of the form:
Volatility
[
τ
,
τ
′
,
p
;
z
]
=
MNorm
[
τ
2
,
p
;
Δ
[
τ
′
;
z
]
]
,
where
MNorm[τ,p;z]=MA[τ;|z| p ] 1/p , and
MA
[
τ
,
n
]
=
1
n
∑
k
=
1
n
EMA
[
τ
′
,
k
]
with
τ
′
=
2
τ
n
+
1
,
and where p satisfies 0<p≦2, and τ′ is a time horizon of a return r[τ]=Δ[τ; x], where x represents a logarithmic price.
9 . The method of claim 1 , wherein said exponential moving average operator EMA[τ; z] has the form:
EMA[τ;z]=μEMA[τ;z ]( t n−1 )+( v −μ) z n−1 +(1− v ) z n where
α
=
t
n
-
t
n
-
1
τ
μ=e −α , and
v
=
1
-
μ
α
,
corresponding to a linear interpolation procedure.
10 . The method of claim 1 , wherein said exponential moving average operator EMA[τ; z] has the form:
EMA[τ;z]=μEMA[τ;z] ( t n−1 )+( v−μ ) z n−1 +(1 −v ) z n where
α
=
t
n
-
t
n
-
1
τ
μ=e −α , and
v=1, corresponding to a previous point interpolation procedure.
11 . The method of claim 1 , wherein said exponential moving average operator EMA[τ; z] has the form:
EMA[τ;z]=μEMA[τ;z ]( t n−1 )+( v −μ) z n−1 +(1 −v ) z n where
α
=
t
n
-
t
n
-
1
τ
μ=e −α , and
v=μ, corresponding to a next point interpolation procedure.
12 . A method of determining value-at-risk, comprising the steps of:
constructing an inhomogeneous time series z that represents received financial market transaction data; constructing an iterated exponential moving average operator; constructing a time-translation-invariant, causal operator Ω[z] that is a convolution operator with kernel ω and that is based on said iterated exponential moving average operator; electronically calculating values of one or more predictive factors relating to said time series z, wherein said one or more predictive factors are defined in terms of said operator Ω[z]; and electronically calculating value-at-risk from said calculated values.Join the waitlist — get patent alerts
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