CA2540433A1 - A system and method of underwriting price risk with and insured window contract - Google Patents

A system and method of underwriting price risk with and insured window contract Download PDF

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CA2540433A1
CA2540433A1 CA 2540433 CA2540433A CA2540433A1 CA 2540433 A1 CA2540433 A1 CA 2540433A1 CA 2540433 CA2540433 CA 2540433 CA 2540433 A CA2540433 A CA 2540433A CA 2540433 A1 CA2540433 A1 CA 2540433A1
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account
contract
window
trust account
trust
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French (fr)
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Charles W. Grant
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06QINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00Finance; Insurance; Tax strategies; Processing of corporate or income taxes

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  • Accounting & Taxation (AREA)
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  • Physics & Mathematics (AREA)
  • General Business, Economics & Management (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Financial Or Insurance-Related Operations Such As Payment And Settlement (AREA)

Abstract

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. 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.

Description

. V 1 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 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.

.. ~ ,, _ .. , ~ . . i . , .

(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.

., ~ õ , 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.

, , i 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~"

(2cos (s7r~ - 67r~ - (-2cos (6) - 6) _ (-2(-~) - s~] - [-2(~) - s) -s7r+~+s = 2v/'3- - 37r = 1.369706513 ~ ~.
~ --~ ~~ ~~ , ~ ~

., i . i .

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 , , , 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.

., ~ , . 1 . . . 1 1~ -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

Claims (26)

1. A system and method of underwriting price risk with an insured window con-tract that comprises the steps of:
2 (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 operating account as part of on-going operations.
(e) Participants hold interest in their trust account assigned to the contract, 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 and named beneficiary should there be a claim.
(g) Trust 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 going 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.
(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.
3 (p) When the market price x is between x- and x+, the buyer and seller realize 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.

2. The system and method in claim 1(a), wherein said buyers/sellers include, but are not limited to, buyers/sellers of stocks, commodities and/or any other se-curity or non-security that has a market price that is volatile, well-defined, transparent and cannot be influenced by individual buyers/sellers in the mar-ketplace.

3. The system and method in claim 1(a), wherein said continous volume may or may not be discretized.
4. The system and method in claim 1(a), wherein contract duration is determined, but not limited to, a negotiated agreement between the buyer/seller and under-writer of the insured window contract.
5. The system and method in claim 1(b), wherein said markets may or may not be comprised of exchange traded instruments.
6. The system and method in claim 1(c), wherein said operating account and trust account are established by the participant to facilitate money flows.
7. The system and method in claim 1(c), wherein said operating account and trust account may or may not be held in a common financial institution.
8. The system and method in claim 1(f), wherein said indemnity agreement is established, exercisable on the day of contract expiry.
9. The system and method of claim 1(f), wherein said trust account is the deemed policy holder and beneficiary of indemnity should there be a claim.
10. The system and method of claim 1(g), wherein said trust account surpluses are held as interest-bearing risk-free deposits invested in a designated financial institution.
11. The system and method of claim 1(h), wherein said trust account deficits may or may not be financed as the same designated financial institution as named in 1(g).
12. The system and method of claim 1(i), wherein said financial institution may or may not take security in the indemnity agreement.
13. The system and method of claim 1(j), wherein the window is set actuarially so the trust account is expected to be (but not guaranteed to be) left with zero balance at the end of the multi-period contract.
14. The system and method of claim 1(k), wherein the window is set, at the begin-ning 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.
15. The system and method of claim 1(1), wherein 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.
16. The system and method of claim 1(m), wherein 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.
17. The system and method of claim 1(n), wherein 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.
18. The system and method of claim 1(o), wherein 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.
19. The system and method of claim 1(p), wherein when the market price x is between x- and x+, the buyer and seller realize their transactions at x and there is no activity in terms of transfers between the operating account and trust account.
20. The system and method of claim 1(q), wherein if reality varies from the actuarial projection, the trust account could be in surplus or deficit at the time of contract expiry.
21. The system and method of claim 1(r), wherein the surplus in the trust account at contract expiry is transferred out to the operating account to leave the trust account with zero balance.
22. The system and method of claim 1(s), wherein a deficit in the trust account at contract expiry is brought to zero with the process described below.
23. The system and method of claim 1(t), wherein the first monies towards the deficit come from retention within the trust itself (a deductible).
24. The system and method of claim 1(u), wherein the second monies towards a deficit come from the primary insurer.
25. The system and method of claim 1(v), wherein the third monies towards a deficit come from reisurers.
26. The system and method of claim 1(w), wherein the buyers and sellers pay a premium up front for coverage under the indemnity agreement, possibly financed by a designated bank, with repayment monies being drawn out of the operating account over time.
CA 2540433 2006-03-17 2006-03-17 A system and method of underwriting price risk with and insured window contract Abandoned CA2540433A1 (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106844544A (en) * 2016-12-30 2017-06-13 全民互联科技(天津)有限公司 A kind of contract terms Risk Identification Method and system

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106844544A (en) * 2016-12-30 2017-06-13 全民互联科技(天津)有限公司 A kind of contract terms Risk Identification Method and system

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