Note: Descriptions are shown in the official language in which they were submitted.
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CA 02540433 2006-03-17
Field of the Invention
The invention is a system and method of underwriting price risk with an
insured
window contract. It is in, but not limited to, the fields of financial
engineering and
financial risk management.
6 Background of the Invention
Buyers and sellers in open market economies face price risk if the asset is
volatile in
price over time. Oftentimes, price coverage is required by buyers and sellers
to facil-
itate planning and operations and to protect profits. The insured window
contract
gives the buyers and sellers a new method and system to underwrite price risk.
Ex-
isting methods include financial derivatives like forwards, futures and
options, offered
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in exchange-traded or over-the-counter markets. The insured window contract is
an
addition to that suite of choices.
7 Summary of the Invention
1. A system and method of underwriting price risk with an insured window con-
tract that comprises the steps of:
(a) Buyers/sellers enter into a multi-period contract for a continuous volume
of purchases/sales at market prices of the day over the contract period.
(b) Market prices are well-defined, transparent, and cannot be influenced by
individual buyers or sellers.
(c) Buyers and sellers participating in the insured window contract establish
an operating account and a trust account.
(d) Participants hold interest in their own operating account as part of on-
going operations.
(e) Participants hold interest in their own trust account assigned to the con-
tract, whether in surplus or deficit.
(f) An indemnity agreement, exercisable on the day of contract expiry, is
struck with the trust account as policy holder.
(g) TYust account surpluses are held as interest-bearing risk-free deposits in-
vested in a designated financial institution.
(h) Trust account deficits are financed by the same financial institution as
above at pre-arranged interest rates.
(i) The designated financial institution takes security in the indemnity agree-
ment.
(j) The window is set actuarially so the trust account is expected to be left
with a zero balance at the end of the multi-period contract.
(k) The window is set, at the beginning of the multi-period contract period
for the contract period, such that x+ is the top of the window and x- is
the bottom of the window.
(1) When the market price x rises above x+, the buyer pays the market price x
and the difference between x and x+ is transferred from the trust account
to the operating account.
(m) When the market price rises above x+, the seller receives the market price
x and the difference between x and x+ is transferred from the operating
account to the trust account.
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CA 02540433 2006-03-17
(n) When the market price falls below x-, the buyer pays the market price
x and the difference between x- and x is transferred from the operating
account to the trust account.
(o) When the market price falls below x-, the seller receives the market price
x and the difference between x- and x is transferred from the trust account
to the operating account.
(p) When the market price x is between x- and x+, the buyer and seller do
their transactions at x and there is no activity in terms of transfers between
the operating account and trust account.
(q) If reality varies from the actuarial projection, the trust account could
be
in surplus or deficit at the time of contract expiry.
(r) A surplus in the trust account at contract expiry is transferred out to
the
operating account to leave the trust account with zero balance.
(s) A deficit in the trust account at contract expiry is brought to zero with
the process described below.
(t) The first monies towards the deficit come from retention within the trust
itself (a deductible).
(u) The second monies towards a deficit come from the primary insurer.
(v) The third monies towards a deficit come from reisurers.
(w) Buyers and sellers pay a premium up front for coverage under the indem-
nity agreement, possibly financed by a designated bank, with repayment
monies being drawn out of the operating account over time.
8 Preferred Embodiments
The invention embodies a system and method of underwriting price risk with an
insured window contract. The system and method has application in any
marketplace
where there is a transparent price that exhibits volatility over time. It is
applicable
to both buyers and sellers facing price risk in the marketplace.
A window is established which specifies a minimum and maximum price. Market
prices outside the window result in a deposit to or withdrawl from a trust
account
fully owned by the participant in the insured window contract. The trust
account
is established to hold surpluses and deficits over the life of the contract,
normally of
multi-period duration. An operating account, also fully owned by the
participant,
is also established to serve as the participant's operational account and to
receive
monies from and transfer monies to the trust account.
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On the buyer side, market prices below the window cause monies equal to the
difference between market price and minimum of the window to be transferred
from
the operational account to the trust account, whereas market prices above the
window
cause monies equal to the difference between the market price and maximum of
the
window to be transferred from the trust account to the operational account. On
the seller side, market prices below the window cause monies equal to the
difference
between market price and minimum of the window to be transferred from the
trust
account to the operational account, whereas market prices above the window
cause
monies equal to the difference between the market price and maximum of the
window
to be transferred from the operational account to the trust account.
Surpluses or deficits accrue in the trust account over the duration of the
contract.
At contract expiry, surpluses are transferred to the operational account to
bring the
trust account to a zero balance. At contract expiry, deficits are indemnified
by a
pre-arranged insurance policy above some retention of risk (deductible) also
to bring
the trust account to a zero balance.
The insurance policy is put in place at the outset of the contract and comes
with
consideration in the form of payment of a premium. The premium may be financed
with a repayment scheme structured over the life of the contract. Arrangement
for
contingent financing of the deficit is also arranged at the outset of the
contract. The
finacier's interests are secured by the insurance policy's guarantee of
indemnification
at the contract's expiry should there be a deficit at that time.
The following is a simple mathematical model of the system and method of un-
derwriting price risk with an insured window contract. As with any model, it
is an
extraction from reality but provides some insight and is an aid to discussion
of the
insured window.
Let's say commodity prices over time can be described with the equation,
y = 2sin(x) (1)
where time is measured along the x-axis in units of pi and spot price is
measured
along the y-axis in monetary units. One price cycle is represented by 2pi
along the
x-axis. The window stretches along the y-axis from y = -1 to y = +1. A surplus
is
accumulated when the spot price is above the window and the producer receives
the
upper-window price (+1) despite the spot price being higher; a deficit
accumulates
when the spot price is below the window and the producer receives the lower-
window
price (-1) despite the spot price being lower. The surplus/deficit are
represented by
the shaded areas above/below the window.
The area A+ above the upper-window and below the spot price represents the
surplus; the area A- below the lower window and above the spot price
represents the
deficit. Due to symmetry of the function, both areas are equal.
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CA 02540433 2006-03-17
The coordinates of the points of intersection of the spot price function, y =
2sinx,
and the upper level window, y = 1, are determined as follows:
2sinx = 1 (2)
sinx = 2
x = sin-1(2)
(6~ 1)> ts7, 1)
The following integration is used to determine the area A+ (which is
equivalent
to A-):
A+ = Zz [(2sinx) -1]dx (3)
_ {-2cosx - x}I~"
6
(2cos (s7r~ - 67r~ - (-2cos (6) - 6)
_ (-2(-~) - s~] - [-2(~) - s)
-s7r+~+s
= 2v/'3- - 37r
= 1.369706513
~ ~.
~ --~ ~~ ~~ , ~ ~
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CA 02540433 2006-03-17
Obviously, spot prices movements do not follow a nice sin curve as is
suggested
by the model; an assessment of actual historical spot prices is needed for a
complete
study (it is presented later in the paper). The simple model does, however,
provided
some useful functions - it outlines the processes of measuring surpluses and
deficits
and illustrates the concept of surplus-deficit balance, both central to our
discussion.
Over the duration of the window contract, the cummulative gross income earned
is described with the equation:
t t ~ s(n) < s)(4)
Y(1) = x ~ s(n) + z ~ ((s+ - s(n) I s(n) > s+) +(S(n) - s
where
Y(i) is the cummulative gross income earned over the duration of the window
con-
tract,
x is the number of units of stock sold per time period t,
S(n) is the price of the stock at time period n,
S+ is the price specified as the top of the window,
S- is the price specified as the bottom of the window,
z is the number of units of stock contracted with the window per time period
t.
At contract expiry:
let
n
W = x E S(n) (5)
t=1
and
Q= z tE I(S+ - S(n) IS(n) > S+) + (S(n) - S-IS(n) < S-)~ (6)
then
Y(n)=W+(QIQ?0)+(Q-I)IQ<0); j=IQI (7)
where Y(n) is the cummulative gross income earned over the contract duration
in-
cluding the end of the contract period and I is the indemnity realized under
the
insured window should there be a deficit at the end of the contract period.
Market price movements do not follow a nice sin curve as is suggested by the
model; market prices can be said to follow a random-walk process. The
stochastic
nature of market prices makes it a challenge to actuarially set the insured
window at
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CA 02540433 2006-03-17
the outset of the contract a challenge. If reality varies from the actuarial
projection
(the insured window is set too high or too low), the trust account could be in
surplus
or deficit at the time of contract expiry. A surplus in the trust account at
contract
expiry is transferred out to the operating account to leave the trust account
with
zero balance. A deficit in the trust account at contract expiry is brought to
zero as
follows: the first monies towards the deficit come from retention within the
trust itself
(a deductible); the second monies towards a deficit come from the primary
insurer;
the third monies towards a deficit come from reisurers. Buyers and sellers pay
a
premium paid up front for the indemnity agreement.
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3 References Cited: Canadian Patent Documents
CA 2429398 Method and System for Simulating Implied Volatility Surfaces for
Basket
Option Pricing
CA 2196042 A System and Method for Purchasing Expirationless Options
CA 2209897 A System and Method for Data Processing of Option/Share Pooling,
And a Method for Conducting Business
CA 2209897 System and Method for Risk Transfer and Diversification Through the
Use of Assurance Accounts
CA 2474662 Business Enterprise Risk Model and Method
CA 2362430 System for Enabling Smaller Investors to Manage Risk
CA 2494567 Method, System and Apparatus for Forming an Insurance Program
