System and method for calculating intra-period volatility

• US 20040034587A1
• Filed: 08/19/2002
• Published: 02/19/2004
• Est. Priority Date: 08/19/2002
• Status: Abandoned Application

• Current Assignee: Option Research and Technology Services LLC
• Original Assignee: Option Research and Technology Services LLC
• Inventors: Amberson, Matthew Gilbert, Pierce, Brian Patrick
• Application Number:
  US10/223,549
• Publication Number:
  US 20040034587A1
• Time in Patent Office: Days
• US Class Current: 705/36
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

Abstract

Disclosed is a system and method for calculating an intra-period volatility of a security. The system includes a means for collecting tick or selected time interval data from a data source, an interface or storage means for collecting or retrieving assumptions and variables used in the determination, and a processor programmed to perform iterative processes to determine the intra-period volatility and perform uses thereof. The steps of the method include receiving tick or selected time interval data from a data source, retrieving or inputting a set of assumptions for use in the calculations, simulating entering into a spread of options, and iteratively adjusting a variable in a pricing model to produce an intra-period volatility. The method may also include using the intra-period volatility in variety of option-related activities.

Claims

1. A method of determining an intra-period volatility of a security, the method comprising the steps of:

(a) selecting a period;

(b) acquiring tick data from a data source;

(c) selecting a set of hedging intervals within the period;

(d) selecting a hedging strategy;

(e) selecting an amount of Gamma for a theoretical option position;

(f) iteratively running a simulation at each hedging interval;

(g) calculating a hedging profit or loss at each simulation;

(h) calculating a number of options to enter into a theoretical option position having the selected amount of Gamma;

(i) calculating a premium over parity cost of the options in the theoretical option position;

(j) iteratively adjusting an at-the-money volatility in a selected valuation model until the pop cost for the theoretical position equals the hedging profit or loss; and

(k) setting the intra-period volatility to the at-the-money volatility when the pop cost for the theoretical position equals the hedging profit or loss.

2. The method of claim 1, wherein the tick data is filtered after being acquired.

3. The method of claim 1, wherein the hedging interval is based on a selected fixed increment.

4. The method of claim 1, wherein the hedging interval is calculated using a method based on standard deviation.

5. The method of claim 4, wherein a historical volatility used to calculate the hedging interval is an at-the-money volatility received from a data service.

6. The method of claim 4, wherein a historical volatility used to calculate the hedging interval is a close-to-close volatility from a number of days prior to a date of calculating the intra-period volatility.

7. The method of claim 4, wherein a daily standard deviation used to calculate the hedging interval is calculated by dividing a selected volatility by a square root of a number of trading days in a year multiplied by a previous day'"'"'s closing price.

8. The method of claim 7, wherein the hedge interval is set to a selected percentage of the daily standard deviation.

9. The method of claim 1, wherein the hedging strategy is based on a trader holding a long option position and making adjustments to the long option position when the hedge interval is reached.

10. The method of claim 1, wherein the hedging strategy is based on a trader holding a short option position and making adjustments to the short option position when the hedge interval is reached.

11. The method of claim 1, wherein the development of the theoretical option position is further comprised of using a calculated guess volatility to enter a position consisting of a number of options having strikes spaced at maximum of either a selected currency amount or a value of the security multiplied by an at-the-money volatility multiplied by a factor.

12. The method of claim 11, wherein a time to expiration for the options in the theoretical option position is selected at a length where the marginal change of daily decay with changes in the time to expiration is minimal.

13. The method of claim 11, wherein a time to expiration for the options in the theoretical option position is a number of business days.

14. The method of claim 11, wherein the number of options in the theoretical option position is calculated by iteratively adjusting a number of options until a total amount of Gamma for the options in the theoretical option position is approximately equal to the amount of Gamma.

15. The method of claim 11, wherein the at-the-money volatility is retrieved from a data service.

16. The method of claim 11, wherein the at-the-money volatility is calculated using the last twenty days close-to-close volatility.

17. A method of determining an intra-period volatility of a security, the method comprising the steps of:

(a) selecting a period;

(b) acquiring options from a data source;

(c) selecting a set of hedging intervals within the period;

(d) selecting a hedging strategy;

(e) selecting an amount of Gamma for a theoretical option position;

(f) iteratively running a simulation at each hedging interval;

(g) calculating a scalping profit or loss at each simulation;

(h) calculating a number of options to enter into a theoretical option position having the amount of Gamma by iteratively adjusting a number of options until a total amount of Gamma for the options in the theoretical option position is approximately equal to the amount of Gamma;

(i) calculating a premium over parity cost for the options in the theoretical option position;

(j) iteratively adjusting an at-the-money volatility in a selected valuation model until the pop cost for the theoretical position equals the hedging profit or loss;

(k) setting the intra-period volatility to the at-the-money volatility when the pop cost for the theoretical position equals the hedging profit or loss; and

(l) making an options-related use of the intra-period volatility.

18. The method of claim 17, wherein the options-related use is to adjust a theoretical value of an option.

19. The method of claim 17, wherein the options-related use is to determine an efficiency of an option market maker.

20. The method of claim 17, wherein the options-related use is to use the intra-period volatility in a forecast model.

21. The method of claim 17, wherein the options-related use is to determine the risk of a position in the security.

22. A system for determining an intra-period volatility of a security comprising:

means for storing data, an output interface for prompting a user for calculation-determinative assumptions and receiving those assumptions from the user;

a means for receiving data;

memory;

a program module;

an input device;

a processor responsive to a plurality of instructions from the program module, being operative to;

prompt the user via an output interface for a period;

receive by a first signal from the input device the period;

receive tick data from a data source;

prompt the user via an output interface for instructions for a hedging interval;

receive by a second signal from the input device the instructions for the hedging interface;

prompt the user via the output interface for instructions for a hedging strategy;

receive by a third signal from the input device the instructions for the hedging strategy;

prompt the user via the output interface for an amount of Gamma;

receive by a fourth signal from the input device the amount of Gamma;

run iteratively a simulation on the tick data utilizing the hedging strategy at each hedging interval;

calculate a hedging profit or loss at each simulation;

prompt the user via the output interface for instructions for a valuation model and receive by a fifth signal from the input device the instructions for the valuation model;

simulate entering into a theoretical option position of options having the amount of Gamma;

adjust iteratively the number of options in the theoretical option position until a total Gamma in the theoretical option position equals the amount of Gamma;

store the number of options on the means for storing data;

calculate a premium over parity cost for the options in the theoretical option position and store the premium over parity cost on the means for storing;

adjust iteratively an at-the-money volatility in a selected valuation model until the pop cost for the theoretical position equals the hedging profit or loss; and

set the intra-period volatility to the at-the-money volatility when the pop cost for the theoretical position equals the hedging profit or loss.

23. The system of claim 22, wherein the processor is also operative to filter the tick or selected time interval data.

24. A system for determining an intra-period volatility of a security comprising:

means for storing data, a means for receiving data;

memory;

a program module;

a processor responsive to a plurality of instructions from the program module, being operative to;

retrieve a period

receive tick data from a data source;

retrieve a set of hedging intervals from the memory;

retrieve a hedging strategy from the memory;

retrieve an amount of Gamma from the memory;

run iteratively a simulation on the tick data utilizing the hedging strategy at each hedging interval;

calculate a hedging profit or loss at each simulation;

retrieve a formula for a valuation model;

simulate entering into a theoretical option position with a number of options;

adjust iteratively the number of options until a total Gamma in the theoretical option position equals the amount of Gamma;

store the number of options on the means for storing;

calculate a premium over parity cost for the options in the theoretical option position and store the premium over parity cost on the means for storing;

adjust iteratively an at-the-money volatility in the formula for the valuation model until the pop cost for the theoretical position equals the hedging profit or loss; and

set the intra-period volatility to the at-the-money volatility when the at-the-money volatility equals the scalping profit.

25. The system of claim 24 wherein the processor is also operative to filter the tick data.

26. The system of claim 24 wherein the processor further operative to produce a carrier wave comprising:

instructions for receiving an object transmitted via carrier wave and an object representing the intra-period volatility.

27. A computer program product for use with a computer, said computer program product comprising:

a module for storing and retrieving a period;

a module for accessing tick data from external source;

a module for storing and retrieving a set of hedging intervals;

a module for storing and retrieving a hedging strategy;

a module for iteratively running a simulation on the tick or selected time interval data utilizing the hedging strategy at each hedging interval;

a module for calculating a hedging profit or loss at each simulation;

a module for storing and retrieving an amount of Gamma from the memory;

a module for simulating entering into a theoretical option position with a number of options to be stored on the means for storing having the amount of Gamma;

a module for calculating a premium over parity cost for the options in the theoretical option position and storing and retrieving the premium over parity cost;

a module for storing and retrieving formula for a valuation model;

a module for adjusting iteratively an at-the-money volatility in the formula for the valuation model until the pop cost for the theoretical position equals the hedging profit or loss;

a module for setting the intra-period volatility to the at-the-money volatility when the pop cost for the theoretical position equals the hedging profit or loss and storing and retrieving the intra-period volatility;

28. The computer program product of claim 27 further comprising a module for outputting the intra-period volatility.

29. A-data-signal embodied in a carrier wave claim comprising:

instructions for receiving objects transmitted by carrier wave and an intra-period volatility value, the intra-period volatility including;

a period;

tick data;

a hedging interval;

a hedging strategy, wherein a simulation and calculation of a hedging profit or loss is performed at each hedge interval using the hedging strategy;

a selected an amount of Gamma;

a theoretical option position containing an amount of options having the amount of Gamma; and

an at-the-money volatility wherein a premium over parity cost for the options in the theoretical option position is equal to a hedging profit or loss.