Method and system for creating and trading derivative investment instruments based on an index of collateralized options

• US 7,949,586 B2
• Filed: 01/28/2008
• Issued: 05/24/2011
• Est. Priority Date: 01/30/2007
• Status: Active Grant

• Current Assignee: HID Global GmbH (Assa Abloy AB), Cboe Exchange, Inc. (Cboe Global Markets, Inc.)
• Original Assignee: Chicago Board Options Exchange Incorporated (Cboe Global Markets, Inc.)
• Inventors: Shalen, Catherine T.
• Primary Examiner(s): Colbert; Ella
• Assistant Examiner(s): Anderson; John A
• Application Number:
  US12/020,809
• Publication Number:
  US 20080183640A1
• Time in Patent Office: 1,212 Days
• Field of Search: 705/35
• US Class Current: 705/35
• CPC Class Codes: G06Q 10/087 Inventory or stock management, e.g. order filling, procurement or balancing against orders
• CPC Class Codes: G06Q 40/00 Finance; Insurance; Tax strategies; Processing of corporate or income taxes
• CPC Class Codes: G06Q 40/04 Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

Abstract

Collateralized option index derivative investment instruments and methods for creating a collateralized option index are disclosed herein based on changes in a performance of collateralized option strategies. According to an aspect of the disclosure, a method for calculating a collateralized option index is disclosed. In one embodiment, the method for calculating a collateralized option index includes calculating a value of a portfolio invested in a collateralized short strategy according to the relation:
V_t=M_t−N_lastP_t
where M_t is a value of a LIBOR component of the portfolio at the close of date t, N_last is a number of put options sold at a last roll date, and P_t is a price of the underlying option portfolio based on arithmetic averages of the last bid and ask prices of all options in the underlying option portfolio reported before a time on date t.

Claims

1. A computer-readable memory containing processor executable program instructions for creating a collateralized option index according to the following steps:

calculating a value of a portfolio invested in a collateralized short strategy according to a relation;

V_t=M_t−

N_oldP_t

wherein M_t is a value of a LIBOR component of the portfolio at a close of date t, N_old is a number of put options sold at a last roll date, and P_t is a price of an underlying option portfolio based on arithmetic averages of last bid and ask prices of all options in the underlying option portfolio reported before a time on date t.

2. The computer-readable memory according to claim 1, wherein on dates other than roll dates a value of the LIBOR component is equal to:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>

wherein ρ

<sub>t−

1,t</sub> is an effective LIBOR rate from date t−

1 to date t.

3. The computer-readable memory according to claim 2, wherein on roll dates cash outflow from a final settlement of expiring options is debited from an account and proceeds from sales of new put options is credited to the account according to a relation:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>−

N_oldMax[0,K_old−

SOQ_t]+N_newP_vwap

where K_old is a strike price of put options sold at a previous roll date, SOQ_t is a final settlement price of these options on date t, N_new is a number of new puts sold and P_vwap is a volume-weighted average price at which the new options are sold.

4. The computer-readable memory according to claim 3, wherein the number N_new is determined according to a relation:

N_new=(M<sub>t−

1</sub>(1+ρ

<sub>t−

1,t</sub>)−

N<sub>t−

1</sub>max[0,K_old−

SOQ_t])/(K_new/(1+r)−

P_vwap)

wherein K_new is a strike price at which new puts are sold, and r is an effective LIBOR rate of return from a present roll date to a next roll date; and

wherein r results from compounding the rate ρ

<sub>t−

1,t</sub> daily from roll date t to the next roll date.

5. A computer-readable memory containing processor executable program instructions for creating a collateralized option index according to the following steps:

calculating a value (V_t) of a portfolio invested in a collateralized short strategy according to a relation;

V_t=M_t−

N_oldP_t

wherein M_t is a value of a money market component of the portfolio at a close of date t, N_old is a number of put options sold at a previous roll date, and P_t is a price of an underlying option portfolio based on arithmetic averages of last bid and ask prices of all options in the underlying option portfolio reported before a time on date t.

6. The computer-readable memory according to claim 5, wherein on dates other than roll dates the value of a LIBOR component is equal to:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>

wherein ρ

<sub>t−

1,t</sub> is an effective LIBOR rate from date t−

1 to date t.

7. The computer-readable memory according to claim 5, wherein on roll dates a value of a money market account includes a cash settlement from expiring put options and proceeds from sales of new put options according to a relation:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>−

N_oldMax[0,K_old−

SOQ_t]+N_newP_vwap

where K_old is a strike price of the put options sold at the previous roll date, SOQ_t is the final settlement price of these options on roll date t, N_new is a number of new puts sold and P_vwap is a volume-weighted average price at which these options are sold.

8. The computer-readable memory according to claim 7, wherein the number Nnew is determined according to a relation:

N_new=(M<sub>t−

1</sub>(1+ρ

<sub>t−

1,t</sub>)−

N<sub>t−

1</sub>max[0,K_old−

SOQ_t])/(K_new/(1+r)−

P_vwap)

wherein K_new is a strike price at which new puts are sold, and r is an effective LIBOR rate of return from a present roll date to a next roll date; and

wherein r results from compounding the rate ρ

<sub>t−

1,t</sub> daily from roll date t to the next roll date.

9. A computer-readable memory containing processor executable program instructions for creating a collateralized option index according to the following steps:

calculating a value (Vt) of a portfolio invested in a collateralized short strategy according to a relation;

V_t=M_t−

N_oldP_t

wherein M_t is a value of a money market component of the portfolio at a close of date t, N_old is a number of bear spreads sold at a previous roll date, and P_t is a value of the bear spread at the close, equal to a difference between arithmetic averages of last bid and ask prices of at-the-money and out-of-the-money put options reported before a time on date t.

10. The computer-readable memory according to claim 9, wherein on dates other than roll dates a value of a LIBOR component is equal to:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>

wherein ρ

<sub>t−

1,t</sub> is an effective LIBOR rate from date t−

1 to date t.

11. The computer-readable memory according to claim 10, wherein on roll dates a value of a money market account includes a cash settlement from an expiring put options and proceeds from a sale of new bear spreads according to a relation:

N_new=(M<sub>t−

1</sub>(1+ρ

<sub>t−

1,t</sub>)−

N<sub>t−

1</sub>(max[0, K_old^atm−

SOQ_t]−

max[0,k_old^otm−

SOQ_t])/((K_new^atm−

K_new^otm)/(1+r)−

P_vwap)

wherein K_new^atm and K_new^otm are strike prices at which the new puts are sold and bought respectively; and

wherein r is the effective LIBOR rate of return from roll date t to the next roll date.

12. The computer-readable memory according to claim 11, wherein the number N_new is determined according to a relation:

N_new=(M<sub>t−

1</sub>(1+ρ

<sub>t−

1,t</sub>)−

N<sub>t−

1</sub>max[0,K_old−

SOQ_t])/(K_new/(1+r)−

P_vwap)

wherein K_new is a strike price at which new puts are sold, and r is an effective LIBOR rate of return from a present roll date to a next roll date; and

wherein r results from compounding the rate ρ

<sub>t−

1,t</sub> daily from roll date t to the next roll date.

13. A computer system for calculating a collateralized option index, the computer system comprising:

a processor configured to determine a value (V_t) of a portfolio invested in a collateralized short strategy according to a relation;

V_t=M_t−

N_oldP_t

wherein M_t is a value of a LIBOR component of the portfolio at a close of date t, N_old is a number of put options sold at a last roll date, and P_t is a price of an underlying option portfolio based on arithmetic averages of last bid and ask prices of all options in the underlying option portfolio reported before a time on date t; and

a communications interface configured to transmit the value of the portfolio in the collateralized short strategy to market participants over a communication network.

14. The computer system according to claim 13, wherein on dates other than roll dates the value of the LIBOR component is equal to:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>

wherein ρ

<sub>t−

1,t</sub> is an effective LIBOR rate from date t−

1 to date t.

15. The computer system according to claim 14, wherein on roll dates, cash outflow from a final settlement of expiring options is debited from an account and proceeds from sales of new put options is credited to the account according to a relation:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>−

N_oldMax[0,K_old−

SOQ_t]+N_newP_vwap

wherein K_old is a strike price of put options sold at a previous roll date, SOQ_t is a final settlement price of these options on date t, N_new is a number of new puts sold and P_vwap is a volume-weighted average price at which the new options are sold.

16. The computer system according to claim 15, wherein the number Nnew is determined according to a relation:

N_new=(M<sub>t−

1</sub>(1+ρ

<sub>t−

1,t</sub>)−

N<sub>t−

1</sub>max[0,K_old−

SOQ_t])/(K_new/(1+r)−

P_vwap)

wherein K_new is a strike price at which new puts are sold, and r is an effective LIBOR rate of return from a present roll date to a next roll date; and

wherein r results from compounding the rate ρ

<sub>t−

1,t</sub> daily from roll date t to the next roll date.

17. A computer system for calculating a collateralized option index, the computer system comprising:

a processor configured to calculate a value (Vt) of a portfolio invested in a collateralized short strategy according to a relation;

V_t=M_t−

N_oldP_t

wherein M_t is a value of a money market component of the portfolio at a close of date t, N_old is a number of put options sold at a previous roll date, and P_t is a difference between arithmetic averages of a last bid and ask prices of the put option reported before a time on date t; and

a communications interface configured to transmit the value of the portfolio to market participants over a communication network.

18. The computer system according to claim 17, wherein on dates other than roll dates the value of a LIBOR component is equal to:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>

wherein ρ

<sub>t−

1,t</sub> is an effective LIBOR rate from date t−

1 to date t.

19. The computer system according to claim 18, wherein on roll dates a value of a money market account includes a cash settlement from expiring put options and proceeds from sales of new put options according to a relation:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>−

N_oldMax[0,K_old−

SOQ_t]+N_newP_vwap

wherein K_old is a strike price of the put options sold at the previous roll date, SOQ_t is a final settlement price of these options on roll date t, N_new is a number of new puts sold and P_vwap is a volume-weighted average price at which these options are sold.

20. The computer system according to claim 19, wherein the number N_new is determined according to a relation:

N_new=(M<sub>t−

1</sub>(1+ρ

<sub>t−

1,t</sub>)−

N<sub>t−

1</sub>max[0,K_old−

SOQ_t])/(K_new/(1+r)−

P_vwap)

wherein K_new is a strike price at which new puts are sold, and r is an effective LIBOR rate of return from a present roll date to a next roll date; and

wherein r results from compounding the rate <sub>ρ

t−

1,t</sub> daily from roll date t to the next roll date.

21. A computer system for calculating a collateralized option index, the computer system comprising:

a processor configured to calculate a value of a portfolio invested in a collateralized short strategy according to a relation;

V_t=M_t−

N_oldP_t

wherein M_t is a value of a money market component of the portfolio at a close of date t, N_old is a number of bear spreads sold at a previous roll date, and P_t is a value of the bear spread at a close, equal to a difference between arithmetic averages of last bid and ask prices of at-the-money and out-of-the-money put options reported before a time on date t; and

a communications interface configured to transmit the value of the portfolio to market participants over a communication network.

22. The computer system according to claim 21, wherein on dates other than roll dates a value (M_t) of a LIBOR component is equal to:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>

wherein ρ

<sub>t−

1,t</sub> is an effective LIBOR rate from date t−

1 to date t.

23. The computer system according to claim 22, wherein on roll dates a value of a money market account includes a cash settlement from expiring put options and proceeds from a sale of new bear spreads according to a relation:

M_t=(1+ρ

<sub>t−

1,t</sub>)M<sub>t−

1</sub>−

N_oldMax[0,K_old^atm−

SOQ_t]+N_newP_vwap

wherein K_old^atm is a strike price of the put options sold at the previous roll date, SOQ_t is a final settlement price of these options on roll date t, N_new is the number of new bear spreads sold and P_vwap is a price of the spread based on a volume-weighted average prices at which at-the-money and out-of-the money put options in the spread are sold and bought respectively.

24. The computer system according to claim 23, wherein N_new is a number of new bear spreads sold on roll date t according to a relation:

N_new=(M<sub>t−

1</sub>(1 +ρ

<sub>t−

1,t</sub>)−

N<sub>t−

1</sub>(max[0, K_old^atm−

SOQ_t]−

max[0, K_old^atm−

SOQ_t])/((K_new^atm−

K_new^otm)/(1+r)−

P_vwap)

wherein K_new^atm and K_new^otm are strike prices at which the new puts are sold and bought respectively; and

wherein r is the effective LIBOR rate of return from roll date t to the next roll date.