WO1997007475A1 - Estimation method and system for financial securities trading - Google Patents
Estimation method and system for financial securities trading Download PDFInfo
- Publication number
- WO1997007475A1 WO1997007475A1 PCT/US1995/010363 US9510363W WO9707475A1 WO 1997007475 A1 WO1997007475 A1 WO 1997007475A1 US 9510363 W US9510363 W US 9510363W WO 9707475 A1 WO9707475 A1 WO 9707475A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- points
- producing
- integrand
- computer
- low
- Prior art date
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Classifications
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- 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
- G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
- G06Q40/02—Banking, e.g. interest calculation or account maintenance
Definitions
- the invention relates to financial securities trading such as, e.g., trading in stocks, bonds and financial derivative instruments, including futures, options and collateralized mortgage obligations.
- the value of a security may be estimated, e.g., based on expected future cash flow.
- cash flow may depend on variable interest rates, for example, and these and other relevant variables may be viewed as stochastic variables.
- CMO collateralized mortgage obligations
- instruments or securities variously called tranches, shares, participations, classes or contracts have cash flows which are determined by dividing and distributing the cash flow of an underlying collection or pool of mortgages on a monthly basis according to pre-specified rules.
- the present value of a tranche can be estimated on the basis of the expected monthly cash flows over the remaining term of the tranche, and an estimate of the present value of a tranche can be represented as a multi-dimensional integral whose dimension is the number of payment periods of the tranche. For a typical instrument with a 30-year term and with monthly payments, this dimension is 360.
- such a high-dimensional integral can be evaluated only approximately, by numerical integration. This involves the generation of points in the domain of integration, evaluating or "sampling" the integrand at the generated points, and combining the resulting integrand values, e.g., by averaging.
- Well known for numerical integration in securities trading is the so-called Monte Carlo method in which points in the domain of integration are generated at random.
- a preferred method for estimating the value of a financial security involves numerical integration unlike Monte Carlo integration in that an integrand is sampled at deterministic points having a low-discrepancy property. As compared with the Monte Carlo method, significant advantages are realized with respect to speed, accuracy, and dependability.
- Fig. 1 is a schematic of a programmed computer system in accordance with a preferred embodiment of the invention.
- Fig. 2 is a graphic representation of performance data obtained in computer trial runs with an exemplary embodiment of the invention as compared with two Monte Carlo computations.
- Fig. 1 shows a stored-program computer 11 connected to input means 12, e.g., a keyboard, for entering financial securities data, and connected to output means 13, e.g., a visual display device, for displaying an estimated value of the financial security.
- the computer 11 includes a working memory M, a low-discrepancy deterministic point generator P, an integrand evaluator E, and an integrand-value combiner C.
- sample points correspond to points of a low-discrepancy deterministic sequence in the multivariate unit cube via a suitable
- a low-discrepancy deterministic sequence z 1 , z 2 , ... of points in D can be characterized as follows:
- the sequence z,, z 2 , ... is said to be a low-discrepancy deterministic sequence provided
- CMO FN collateralized mortgage obligation
- the monthly cash flow is divided and distributed according to pre-specified rules which are included in a formal prospectus.
- Some of the basic rules may be stated as follows:
- the coupon is paid to the tranches.
- the remaining amount called Principal Distribution Amount
- the Principal Amount Prior to a fixed date in the future, the Principal Amount will be allocated sequentially to the tranches 23-G, 23-H, 23-J and 23-Z. After that date, the Principal Distribution Amount will be
- the remaining amount of principal borrowed is C ⁇ a k .
- ⁇ 1 , £ 2 , . . . , ⁇ 360 are independent, normally distributed random variables with mean 0 and variance ⁇ , and K 0 is a given constant.
- K 0 is a given constant.
- ⁇ 0.0004 is chosen. It is assumed further that w k as a function of i k can be computed as
- This cash flow is distributed according to the rules of FN, 89-23. Then, the cash flow for each of the tranches is multiplied by the discount factor , to find the present value for month k. Summing of the present values for every month gives the present value PV T , for each tranche T.
- E(PV T ) E(PV ⁇ ( ⁇ 1 ,..., ⁇ 360 )),
- a 360-variate integrand has to be integrated over the 360-dimensional unit cube, .
- Fig. 2 shows results from trial runs for
- Halton points were used as generated by the corresponding computer algorithm given in the Appendix. It is felt that Sobol points may be preferred over Halton points for integrals of high dimension. However, this preference may not apply in the case of lower-dimensional integrals, e.g., with dimension up to 5 or so.
- a computation as described may be terminated after a predetermined number of function evaluations.
- a current approximation may be compared with one or several preceding approximations, for termination once a suitable condition depending on the difference between approximations is met.
- termination criteria may be called automatic. Automatic termination is particularly reliable where a sequence of approximations settles down smoothly; see, e.g., the curve in Fig. 2 corresponding to Sobol points.
- a cluster or network of multiple parallel processors or workstations can be used. This may involve a master or host processor providing points of a low-discrepancy sequence to slave processors and combining function values returned by the slave processors into an
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- Business, Economics & Management (AREA)
- Accounting & Taxation (AREA)
- Finance (AREA)
- Engineering & Computer Science (AREA)
- Development Economics (AREA)
- Economics (AREA)
- Marketing (AREA)
- Strategic Management (AREA)
- Technology Law (AREA)
- 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
Description
Claims
Priority Applications (4)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
PCT/US1995/010363 WO1997007475A1 (en) | 1995-08-15 | 1995-08-15 | Estimation method and system for financial securities trading |
JP9509227A JPH11510931A (en) | 1995-08-15 | 1995-08-15 | Estimation method and system for complex securities using low mismatch deterministic sequences |
EP95928840A EP0845123A4 (en) | 1995-08-15 | 1995-08-15 | Estimation method and system for financial securities trading |
CA002229144A CA2229144C (en) | 1995-08-15 | 1995-08-15 | Estimation method and system for financial securities trading |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
PCT/US1995/010363 WO1997007475A1 (en) | 1995-08-15 | 1995-08-15 | Estimation method and system for financial securities trading |
CA002229144A CA2229144C (en) | 1995-08-15 | 1995-08-15 | Estimation method and system for financial securities trading |
Publications (1)
Publication Number | Publication Date |
---|---|
WO1997007475A1 true WO1997007475A1 (en) | 1997-02-27 |
Family
ID=25680030
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/US1995/010363 WO1997007475A1 (en) | 1995-08-15 | 1995-08-15 | Estimation method and system for financial securities trading |
Country Status (3)
Country | Link |
---|---|
EP (1) | EP0845123A4 (en) |
CA (1) | CA2229144C (en) |
WO (1) | WO1997007475A1 (en) |
Cited By (12)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO1998036364A1 (en) * | 1997-02-14 | 1998-08-20 | Numerix L.L.C. | Quasi-monte carlo integration |
FR2792746A1 (en) * | 1999-04-21 | 2000-10-27 | Ingmar Adlerberg | Control of staged production flow in response to random pressures on production stages using the 'value at risk' method |
EP1079321A1 (en) * | 1994-08-04 | 2001-02-28 | The Trustees of Columbia University in the City of New York | Estimation method and system for complex securities, and portfolio structuring, using low-discrepancy deterministic sequences |
WO2001088829A1 (en) * | 2000-05-18 | 2001-11-22 | Brian Street | System and method for identifying potential participants in a public offering |
US6381586B1 (en) * | 1998-12-10 | 2002-04-30 | International Business Machines Corporation | Pricing of options using importance sampling and stratification/ Quasi-Monte Carlo |
US6393409B2 (en) | 1997-10-31 | 2002-05-21 | Morgan Stanley Dean Witter & Co. | Computer method and apparatus for optimizing portfolios of multiple participants |
EP1232462A2 (en) * | 2000-09-26 | 2002-08-21 | Sylvain Raynes | Inverse solution for structured finance |
US6546375B1 (en) * | 1999-09-21 | 2003-04-08 | Johns Hopkins University | Apparatus and method of pricing financial derivatives |
SG115327A1 (en) * | 1999-08-19 | 2005-10-28 | Univ Columbia | Estimation method and system for complex securities using low-discrepancy deterministic sequences |
US7765133B1 (en) * | 2000-02-16 | 2010-07-27 | Omgeo Llc | System for facilitating trade processing and trade management |
US11170254B2 (en) | 2017-09-07 | 2021-11-09 | Aurora Innovation, Inc. | Method for image analysis |
US11334762B1 (en) | 2017-09-07 | 2022-05-17 | Aurora Operations, Inc. | Method for image analysis |
-
1995
- 1995-08-15 CA CA002229144A patent/CA2229144C/en not_active Expired - Fee Related
- 1995-08-15 EP EP95928840A patent/EP0845123A4/en not_active Withdrawn
- 1995-08-15 WO PCT/US1995/010363 patent/WO1997007475A1/en not_active Application Discontinuation
Non-Patent Citations (7)
Title |
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"MONTE CARLO EVALUATION OF FINITE-DIMENSIONAL INTEGRALS", MONTE CARLO METHODS, XX, XX, 1 January 1986 (1986-01-01), XX, pages 89 - 116, XP002941995 * |
CIPRA B: "MIX WELL, THEN APPLY: MATH MEETING IN D.C.", SCIENCE, AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE, US, vol. 253, 26 July 1991 (1991-07-26), US, pages 384/385, XP002941950, ISSN: 0036-8075, DOI: 10.1126/science.253.5018.384-a * |
NIDERREITER H: "RANDOM NUMBER GENERATION AND QUASI-MONTE CARLO METHODS", JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS., SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, PHILADELPHIA, 1 January 1992 (1992-01-01), PHILADELPHIA, pages I + 01 - 45, XP002943848, ISSN: 0368-4245 * |
PASKOV S H: "AVERAGE CASE COMPLEXITY OF MULTIVARIATE INTEGRATION FOR SMOOTH FUNCTIONS", JOURNAL OF COMPLEXITY, ACADEMIC PRESS, ORLANDO, FL, US, vol. 09, 1 January 1993 (1993-01-01), US, pages 291 - 312, XP002941994, ISSN: 0885-064X, DOI: 10.1006/jcom.1993.1019 * |
See also references of EP0845123A4 * |
WOZNIAKOWSKI H: "AVERAGE CASE COMPLEXITY OF LINEAR MULTIVARIATE PROBLEMS II. APPLICATIONS", JOURNAL OF COMPLEXITY, ACADEMIC PRESS, ORLANDO, FL, US, vol. 08, 1 January 1992 (1992-01-01), US, pages 373 - 392, XP002941997, ISSN: 0885-064X, DOI: 10.1016/0885-064X(92)90002-S * |
WOZNIAKOWSKI H: "AVERAGE CASE COMPLEXITY OF MULTIVARIATE INTEGRATION", BULLETIN, NEW SERIES, OF THE AMERICAN MATHEMATICAL SOCIETY, THE SOCIETY, PROVIDENCE, US, vol. 24, no. 01, 1 January 1991 (1991-01-01), US, pages 185 - 194, XP002941996, ISSN: 0273-0979 * |
Cited By (18)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP1079321A1 (en) * | 1994-08-04 | 2001-02-28 | The Trustees of Columbia University in the City of New York | Estimation method and system for complex securities, and portfolio structuring, using low-discrepancy deterministic sequences |
WO1998036364A1 (en) * | 1997-02-14 | 1998-08-20 | Numerix L.L.C. | Quasi-monte carlo integration |
US6208738B1 (en) | 1997-02-14 | 2001-03-27 | Numerix Corp. | Interface between two proprietary computer programs |
US6393409B2 (en) | 1997-10-31 | 2002-05-21 | Morgan Stanley Dean Witter & Co. | Computer method and apparatus for optimizing portfolios of multiple participants |
US7613652B2 (en) | 1997-10-31 | 2009-11-03 | Morgan Stanley | Computer methods and apparatus for optimizing portfolios of multiple participants |
US6381586B1 (en) * | 1998-12-10 | 2002-04-30 | International Business Machines Corporation | Pricing of options using importance sampling and stratification/ Quasi-Monte Carlo |
WO2000065418A2 (en) * | 1999-04-21 | 2000-11-02 | Billiotte Jean Marie | Method and automatic control for regulating a multiple-stage industrial production controlling random chained stress, application to noise and value at risk control of a clearing house |
FR2792746A1 (en) * | 1999-04-21 | 2000-10-27 | Ingmar Adlerberg | Control of staged production flow in response to random pressures on production stages using the 'value at risk' method |
WO2000065418A3 (en) * | 1999-04-21 | 2001-04-12 | Billiotte Jean Marie | Method and automatic control for regulating a multiple-stage industrial production controlling random chained stress, application to noise and value at risk control of a clearing house |
SG115327A1 (en) * | 1999-08-19 | 2005-10-28 | Univ Columbia | Estimation method and system for complex securities using low-discrepancy deterministic sequences |
US6546375B1 (en) * | 1999-09-21 | 2003-04-08 | Johns Hopkins University | Apparatus and method of pricing financial derivatives |
US7765133B1 (en) * | 2000-02-16 | 2010-07-27 | Omgeo Llc | System for facilitating trade processing and trade management |
WO2001088829A1 (en) * | 2000-05-18 | 2001-11-22 | Brian Street | System and method for identifying potential participants in a public offering |
EP1232462A2 (en) * | 2000-09-26 | 2002-08-21 | Sylvain Raynes | Inverse solution for structured finance |
EP1232462A4 (en) * | 2000-09-26 | 2003-05-21 | Sylvain Raynes | Inverse solution for structured finance |
US11170254B2 (en) | 2017-09-07 | 2021-11-09 | Aurora Innovation, Inc. | Method for image analysis |
US11334762B1 (en) | 2017-09-07 | 2022-05-17 | Aurora Operations, Inc. | Method for image analysis |
US11748446B2 (en) | 2017-09-07 | 2023-09-05 | Aurora Operations, Inc. | Method for image analysis |
Also Published As
Publication number | Publication date |
---|---|
CA2229144A1 (en) | 1997-02-27 |
EP0845123A4 (en) | 2001-04-11 |
CA2229144C (en) | 2002-12-31 |
EP0845123A1 (en) | 1998-06-03 |
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