# US 8,751,371 B2 · Weather derivative volatility surface estimation

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- Number: US 8,751,371 B2
- Document ID: US8751371B2
- Status: Granted
- Kind: B2
- Application number: 14/010,050
- Filed: 2013-08-26
- Published: 2013-12-26
- Granted: 2014-06-10
- Earliest claimed: 2008-08-14
- Assignees: Chicago Mercantile Exchange Inc.
- Applicants: Chicago Mercantile Exchange, Inc.
- Inventors: Muhammed Hadi; Ketan Patel
- Web page: https://patentgrep.com/patent/US8751371B2

## CPC

- G06Q 40/04: Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
- G06Q 40/00: Finance; Insurance; Tax strategies; Processing of corporate or income taxes
- G06Q 40/06: Asset management; Financial planning or analysis
- G06Q 40/08: Insurance
- G06Q: INFORMATION 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

## Abstract

Systems and methods are provided for determining the volatility of weather derivative option contracts. Volatility levels are initially determined with conventional methods. Unreliable volatility levels are then replaced with futures contracts volatility levels. If the futures contracts volatility levels are not available or appear unreliable, meteorological volatility levels are utilized. The data may be reduced to a three dimensional surface and used when determining margin account requirements.

## Claims

### Claim 1

A method of determining a volatility for a group of weather derivative products; the method comprising:
(a) determining at a processor volatility levels for weather derivative option contracts having a range of strike prices and a range of times to maturity using an option volatility model;
(b) identifying at the processor any of the weather derivative option contract volatility levels that deviate from adjoining volatility levels corresponding to weather derivative option contracts by a predetermined threshold;
(c) replacing the volatility levels identified in (b) with weather derivative futures contracts volatility levels for corresponding futures contracts;
(d) displaying an implied volatility surface; and
(e) calculating the amount of credit or risk available using a portfolio risk management determination method and at least one of the volatility levels.

### Claim 2 (depends on 1)

The method of claim 1,
wherein the option volatility model comprises a Black Scholes model.

### Claim 3 (depends on 1)

The method of claim 1,
wherein the option volatility model comprises a Jewson model.

### Claim 4 (depends on 1)

The method of claim 1,
wherein the implied volatility surface includes volatility levels for at least some of the weather derivative option contracts and at least either a volatility level for a weather derivative futures contract from (c).

### Claim 5

A method of determining a margin account requirement for a portfolio that includes at least one weather derivative product, the method comprising:
(a) determining at a processor volatility levels for weather derivative contracts having a range of strike prices and a range of times to maturity using an option volatility model;
(b) identifying at the processor any of the weather derivative option contract volatility levels that deviate from adjoining volatility levels corresponding to weather derivative option contracts by a predetermined threshold;
(c) replacing the volatility levels identified in (b) with futures contracts volatility levels for corresponding futures contracts;
(d) calculating at a processor the amount of credit or risk available using a portfolio risk management determination method and at least one of the volatility levels; and
(e) displaying an implied volatility surface.

### Claim 6 (depends on 5)

The method of claim 5,
wherein the portfolio risk management determination method comprises the Standard Portfolio Analysis of Risk method.

### Claim 7 (depends on 5)

The method of claim 5,
wherein the option volatility model comprises a Black Scholes model.

### Claim 8 (depends on 5)

The method of claim 5,
wherein the option volatility model comprises a Jewson model.

### Claim 9 (depends on 5)

The method of claim 5,
where (c) comprises determining meteorological volatility using a seasonally adjusted GARCH model.

### Claim 10

A non-transitory computer-readable storage medium containing computer-executable instructions for performing the steps comprising:
(a) determining at a processor volatility levels for weather derivative contracts having a range of strike prices and a range of times to maturity using an option volatility model;
(b) identifying weather derivative contract volatility levels that deviate from adjoining volatility levels corresponding to weather derivative option contracts by a predetermined threshold;
(c) replacing the volatility levels identified in (b) with futures contracts volatility levels for corresponding futures contracts;
(d) displaying an implied volatility surface; and
(e) calculating the amount of credit or risk available using a portfolio risk management determination method and at least one of the volatility levels.

### Claim 11 (depends on 10)

The computer-readable medium of claim 10, further including computer-executable instructions for performing:
(d) generating a three-dimensional display of the volatility levels.

### Claim 12 (depends on 10)

The computer-readable medium of claim 10,
wherein the option volatility model comprises a Black Scholes model.

### Claim 13 (depends on 10)

The computer-readable medium of claim 10,
wherein the option volatility model comprises a Jewson model.

### Claim 14 (depends on 11)

The computer-readable medium of claim 11,
wherein the three-dimensional display comprises an implied volatility surface.

### Claim 15 (depends on 10)

The computer-readable medium of claim 10, further including computer-executable instructions for performing:
(d) calculating the amount of credit or risk available using a portfolio risk management determination method and at least one of the volatility levels.

### Claim 16 (depends on 15)

The computer-readable medium of claim 15,
wherein the portfolio risk management determination method comprises the Standard Portfolio Analysis of Risk method.