US 7,925,560 B2Granted

Systems and methods for valuing a derivative involving a multiplicative index

AssigneeMorgan Stanley

InventorsVasily Strela, Matthew Grayson

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Abstract

Methods for calculating a value of a derivative based on a multiplicative index, where the multiplicative index is a multiple of an underlying index. The methods may comprise the steps of providing a first value of the underlying index and estimating a ratio of the multiplicative index over the underlying index as a first function of the underlying index over a first range of values of the underlying index. The method may also comprise the steps of calculating at least one parameter of the first function by comparing the first function to historical values of the multiplicative index and the underlying index. In addition, the method may comprise the steps of calculating a first value for the ratio given the first value of the underlying index, and calculating the value of the derivative for the first value of the ratio.

Claims15

Dependent claims

A computer system for calculating a value of a derivative, the system comprising:

at least one electronic processor and operatively associated memory, wherein the memory comprises instructions that when executed by the processor cause the processor to:
receive data indicating historical values of a first index, wherein the first index indicates an interest rate for tax-exempt municipal bonds;
receive data indicating historical values of a second index, wherein the second index indicates an interest rate for non-tax-exempt instruments;
receive data indicating a value of the second index;
estimate a ratio of the first index over the second index over at least a range of potential values of the second index as an index function, wherein:
the
⁢
⁢
index
⁢
⁢
function
=
(
a
T
⁢
F
T
2
+
b
T
⁢
F
T
+
c
T
)
⁢
Θ
⁡
(
F
T
)
+
(
c
T
-
b
T
2
4
⁢
a
T
)
⁢
(
1
-
Θ
⁡
(
F
T
)
)
the
⁢
⁢
index
⁢
⁢
function
=
1
,
⁢
if
⁢
⁢
F
T
≤
-
b
T
2
⁢
a
T
;
the
⁢
⁢
index
⁢
⁢
function
=
0
⁢
,
⁢
if
⁢
⁢
F
T
>
-
-
b
T
2
⁢
a
T
;
wherein FT is the second index, aT, bT and cT are parameters of the index function, and wherein estimating the ratio comprises calculating aT, bT and cT by comparing the index function to the data indicating historical values of the first index and the data indicating historical values of the second index;
calculate a value for the index function based on the calculated values for aT, bT and cT and the value of the second index;
and
calculate the value of the derivative considering the calculated value of the index function and the value of the second index, wherein the value of the derivative is a function of the first index.

114 more elements

A computer system for calculating a value of a derivative, the system comprising:

at least one electronic processor and operatively associated memory, wherein the memory comprises instructions that when executed by the processor cause the processor to:
receive data indicating historical values of a first index, wherein the first index indicates an interest rate for tax-exempt municipal bonds;
receive data indicating historical values of a second index, wherein the second index indicates an interest rate for non-tax-exempt instruments;
receive data indicating a value of the second index;
estimate a ratio of the first index over the second index over at least a range of potential values of the second index as an index function, wherein:
the
⁢
⁢
index
⁢
⁢
function
=
(
a
T
⁢
F
T
2
=
b
T
⁢
F
T
+
c
T
)
⁢
Θ
⁡
(
F
T
)
+
(
c
T
-
b
T
2
4
⁢
a
T
)
⁢
(
1
-
Θ
⁡
(
F
T
)
)
the
⁢
⁢
index
⁢
⁢
function
=
1
,
if
⁢
⁢
F
T
⁢
<
_
⁢
-
b
T
2
⁢
a
T
;
the
⁢
⁢
index
⁢
⁢
function
=
0
,
if
⁢
⁢
F
T
>
-
b
T
2
⁢
a
T
;
wherein FT is the second index, aT, bT and cT are parameters of the index function, and wherein estimating the ratio comprises calculating aT, bT and cT by comparing the index function to the data indicating historical values of the first index and the data indicating historical values of the second index;
receive a first value function of the derivative, wherein the value function is in terms of the first index;
derive a second value function of the derivative in terms of the second index by substituting the index function into the first value function;
and
calculate the value of the derivative by computing the second value function for the first value of the second index.

114 more elements

Dependencies are inferred from the claim text.