Gamma trading tool

• US 7,418,416 B2
• Filed: 06/20/2001
• Issued: 08/26/2008
• Est. Priority Date: 06/20/2001
• Status: Active Grant

• Current Assignee: Morgan Stanley
• Original Assignee: Morgan Stanley
• Inventors: Guidi, Giovanni, Pauletti, Marco Stephan
• Primary Examiner(s): Cheung; Mary
• Assistant Examiner(s): APPLE, KIRSTEN SACHWITZ
• Application Number:
  US09/885,352
• Publication Number:
  US 20030069826A1
• Time in Patent Office: 2,624 Days
• Field of Search: 705/37, 705/36.R, 705/35
• US Class Current: 705/36.00R
• 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

Automated hedging of financial instruments can include the automated generation of orders to hedge a financial exposure associated with a first financial instrument (e.g., to hedge a risk associated with the value of an option). The hedging orders include buy and sell orders to acquire long or short positions in a hedging instrument having a price movement that is correlated with price movements of the first financial instrument. The long and short positions are acquired so as to offset modeled changes in value of the first financial instrument. After an initial hedging order to buy or sell stock is filled by an exchange, subsequent hedging orders may be generated. Pricing and quantity for the subsequent hedging orders may be based on a user-specified movement in the price of the second financial instrument and may be automatically modified in response to price trending of the market with respect to the second financial instrument.

Claims

1. A computer-implemented method for generating hedging orders, the method comprising:

calculating a volatility factor associated with a first financial instrument;

generating a first stage of a multiple stage hedge sequence, wherein said first stage in the hedge sequence comprises;

a first order to hedge the first financial instrument by acquiring a first position in a second financial instrument at a first target price that is determined based on the volatility factor and a reference price; and

a second order to hedge the first financial instrument by acquiring an opposite position to said first position in the second financial instrument at a second target price that is determined based on said volatility factor and said reference price; and

transmitting the first and second orders to an exchange, such that both the first and the second orders are simultaneously pending and execution of the first or second orders is determined based on price movement of the second financial instrument.

2. The method of claim 1 wherein acquiring a position in the second financial instrument comprises acquiring a position selected from the group consisting of a short position and a long position in the second financial instrument.

3. The method of claim 1 wherein:

the first order comprises a buy order at a target price less than the current asking price.

4. The method of claim 3 wherein said second order to hedge comprises a sell order to sell the second financial instrument at a target price greater than the current bid price for the second financial instrument.

5. The method of claim 1 wherein the first financial instrument comprises an option on an underlying stock and the second financial instrument comprises the underlying stock of the first financial instrument.

6. The method of claim 1 wherein the volatility factor is selected from the group consisting of:

a percMove(σ

) factor, wherein said percMove(σ

) factor represents the daily volatility of the second financial instrument; and

a percMove factor, wherein said percMove factor represents a trader specified value.

7. The method of claim 6, wherein the first order to hedge the first financial instrument by acquiring a first position in a second financial instrument comprises a buy order with a target price, and wherein the target price of said buy order is calculated according to the following formula:

Buy Price=Reference Price*(100−

percMove(σ

))/100.

8. The method of claim 7, further comprising a buy quantity, wherein said buy quantity is calculated according to the following formula:

Buy Qty;

=(percMove(σ

)*Γ

)/Buy Price,

wherein

$\mathrm{\Gamma <br><br>}=\frac{\partial <br><br>\mathrm{\Delta <br><br>}}{\partial <br><br>S}=\frac{\partial <br><br>C^2}{{\partial <br><br>}^2<br><br>S},$

wherein C is the first financial instrument price, S is the second financial instrument price and

$\mathrm{\Delta <br><br>}=\frac{\partial <br><br>C}{\partial <br><br>S}.$

9. The method of claim 8, wherein said opposite position to said first position in the second financial instrument comprises a sell order with a target price and a sell quantity, wherein said target price of said sell order is calculated according to the following formula:

Sell Price=Reference Price*(100+percMove(σ

))/100;

and wherein said sell order quantity is calculated according the following formula;

Sell Qty;

=(percMove(σ

)*Γ

)/Sell Price.

10. The method of claim 6, wherein the first order to hedge the first financial instrument by acquiring a first position in a second financial instrument comprises a sell order with a target price, and wherein the target price of said sell order is calculated according to the following formula:

Sell Price=Reference Price*(100+percMove(σ

))/100.

11. The method of claim 10, further comprising a sell quantity, wherein said sell quantity is calculated according to the following formula:

Sell Qty;

=(percMove(σ

)*Γ

)/Sell Price,

wherein

$\mathrm{\Gamma <br><br>}=\frac{\partial <br><br>\mathrm{\Delta <br><br>}}{\partial <br><br>S}=\frac{\partial <br><br>C^2}{{\partial <br><br>}^2<br><br>S},$

wherein C is the first financial instrument price, S is the second financial instrument price and

$\mathrm{\Delta <br><br>}=\frac{\partial <br><br>C}{\partial <br><br>S}.$

12. The method of claim 10, wherein said opposite position to said first position in the second financial instrument comprises a buy order with a target price and a buy quantity, wherein said target price of said buy order is calculated according to the following formula:

Buy Price=Reference Price*(100−

percMove(σ

))/100

and wherein said buy order quantity is calculated according the following formula;

Buy Qty;

=(percMove(σ

)*Γ

)/Buy Price.

13. A computer-implemented method for generating a sequence of hedging orders to hedge the pricing volatility of a first financial instrument, comprising an option associated with an underlying second financial instrument, the method comprising:

determining a first buy price, a first buy quantity, a first sell price, and a first sell quantity, wherein the first buy price and the first sell price are based on an initial reference price and a volatility factor indicative of the percentage movement in the price of the second financial instrument at which a trader desires to hedge, and wherein the first buy quantity is based on a gamma factor, the volatility factor and the buy price; and

the first sell quantity is based on the gamma factor, the volatility factor and the sell price;

generating a first stage of a hedging sequence for hedging the first financial instrument, the first stage comprising;

a first buy order to purchase the second financial instrument specifying a buy quantity based on the first buy quantity, and a buy price based on the first buy price; and

a first sell order to sell the second financial instrument specifying a sell quantity based on the first sell quantity, and a sell price based on the first sell price; and

transmitting the first buy order and the first sell order to the exchange such that execution of the first buy order or the first sell order is determined based on price movement of the second financial instrument.

14. A computer-implemented system for generating hedging orders, the system comprising:

a programmable processor adapted to;

calculating a volatility factor associated with a first financial instrument;

generating a first stage of a multiple stage hedge sequence, wherein said first stage in the hedge sequence comprises;

a first order to hedge the first financial instrument by acquiring a first position in a second financial instrument at a first target price that is determined based on the volatility factor and a reference price; and

a second order to hedge the first financial instrument by acquiring an opposite position to said first position in the second financial instrument at a second target price that is determined based on said volatility factor and said reference price; and

transmitting the first and second orders to an exchange, such that both the first and the second orders are simultaneously pending and execution of the first or second orders is determined based on price movement of the second financial instrument.

15. The system of claim 14 wherein acquiring a position in the second financial instrument comprises acquiring a position selected from the group consisting of a short position and a long position in the second financial instrument.

16. The system of claim 14 wherein:

the first order comprises a buy order at a target price less than the current asking price.

17. The system of claim 16 wherein said second order to hedge comprises a sell order to sell the second financial instrument at a target price greater than the current bid price for the second financial instrument.

18. The system of claim 14 wherein the first financial instrument comprises an option on an underlying stock and the second financial instrument comprises the underlying stock of the first financial instrument.

19. The system of claim 14 wherein the volatility factor is selected from the group consisting of:

a percMove(θ

) factor, wherein said percMove(θ

) factor represents the daily volatility of the second financial instrument; and

a percMove factor, wherein said percMove factor represents a trader specified value.

20. The system of claim 19, wherein the first order to hedge the first financial instrument by acquiring a first position in a second financial instrument comprises a buy order with a target price, and wherein the target price of said buy order is calculated according to the following formula:

Buy Price =Reference Price *(100- percMove(θ

))/100.

21. The system of claim 20, further comprising a buy quantity, wherein said buy quantity is calculated according to the following formula:

Buy Qty;

=(percMove(θ

)* Γ

)/Buy Price,

wherein

$\mathrm{\Gamma <br><br>}=\frac{\partial <br><br>\mathrm{\Delta <br><br>}}{\partial <br><br>S}=\frac{\partial <br><br>C^2}{{\partial <br><br>}^2<br><br>S},$

wherein C is the first financial instrument price, S in the second financial instrument price and

$\mathrm{\Delta <br><br>}=\frac{\partial <br><br>C}{\partial <br><br>S},$

22. The system of claim 21, wherein said opposite position to said first position in the second financial instrument comprises a sell order with a target price and a sell quantity, wherein said target price of said sell order is calculated according to the following formula:

Sell Price =Reference Price * (100 +percMove(θ

))/100;

and wherein said sell order quantity is calculated according the following formula;

Sell Qty;

=(percMove(θ

) * Γ

)/Sell Price.

23. The system of claim 19, wherein the first order to hedge the first financial instrument by acquiring a first position in a second financial instrument comprises a sell order with a target price, and wherein the target price of said sell order is calculated according to the following formula:

Sell Price =Reference Price * (100 +percMove(θ

))/100.

24. The system of claim 23, further comprising a sell quantity, wherein said sell quantity is calculated according to the following formula:

Sell Qty;

=(percMove(θ

) * Γ

)/Sell Price,

wherein

$\mathrm{\Gamma <br><br>}=\frac{\partial <br><br>\mathrm{\Delta <br><br>}}{\partial <br><br>S}=\frac{\partial <br><br>C^2}{{\partial <br><br>}^2<br><br>S},$

wherein C is the first financial instrument price, S is the second financial instrument price and

$\mathrm{\Delta <br><br>}=\frac{\partial <br><br>C}{\partial <br><br>S},$

25. The system of claim 24, wherein said opposite position to said first position in the second financial instrument comprises a buy order with a target price and a buy quantity, wherein said target price of said buy order is calculated according to the following formula:

Buy Price =Reference Price * (100- percMove(θ

))/100

and wherein said buy order quantity is calculated according the following formula;

Buy Qty;

=(percMove(θ

) * Γ

)/Buy Price.

26. A computer-implemented system for generating a sequence of hedging orders to hedge the pricing volatility of a first financial instrument, comprising an option associated with an underlying second financial instrument, the system comprising:

a programmable processor adapted to;

determining a first buy price, a first buy quantity, a first sell price, and a first sell quantity, wherein the first buy price and the first sell price are based on an initial reference price and a volatility factor indicative of the percentage movement in the price of the second financial instrument at which a trader desires to hedge, and wherein the first buy quantity is based on a gamma factor, the volatility factor and the buy price; and

the first sell quantity is based on the gamma factor, the volatility factor and the sell price;

generating a first stage of a hedging sequence for hedging the first financial instrument, the first stage comprising;

a first buy order to purchase the second financial instrument specifying a buy quantity based on the first buy quantity, and a buy price based on the first buy price; and

a first sell order to sell the second financial instrument specifying a sell quantity based on the first sell quantity, and a sell price based on the first sell price; and

transmitting the first buy order and the first sell order to the exchange such the execution of the first buy order or the first sell order is determined based on price movement of the second financial instrument.