US007171385B1
(12) United States Patent
(10) Patent N0.: (45) Date of Patent:
Dembo et a]. (54)
(75)
SYSTEM AND METHOD FOR TRADING OFF
6,393,409 B2*
PUT AND CALL VALUES OF A PORTFOLIO
6,473,084 B1*
Inventors: Ron S. Dembo, Toronto (CA); Helmut
Mausser, Toronto (CA)
US 7,171,385 B1 Jan. 30, 2007
5/2002 Young ....................... .. 705/37
10/2002 Phillips et al. .
345/440
6,546,375 B1*
4/2003
Pang .............. ..
6,799,167 B1*
9/2004
Gullen et a1. ........... .. 705/36 R
2001/0011243 A1
.. .
705/37
8/2001 Dembo et al.
(73) Assignee: Algorithmics International Corp.,
OTHER PUBLICATIONS
Bridgetown (KN)
Dembo, Ron S., “Mark-to-Future: A Consistent Firm-Wide Para
(*)
Notice:
Subject to any disclaimer, the term of this patent is extended or adjusted under 35
USC 154(b) by 320 days.
Quarterly 3(2), 29-37.
(21) App1.No.: 09/718,500 (22) Filed:
(30)
(Continued)
Nov. 24, 2000
Primary ExamineriElla Colbert (74) Attorney, Agent, or FirmiBereskin & Parr
Foreign Application Priority Data
Nov. 26, 1999
(51)
digm for Measuring Risk and Return”, Risk Management and Analysis. vol. 1: Measuring and Modelling Financial Risk; John Wiley & Sons Lts., 1998, p. 225-236. Dembo, R., Rosen, D. and D. Saunders, 2000, “Valuation in incomplete markets: an optimization approach,” Algo Research
(CA)
.................................. .. 2290888
Int. Cl.
G06Q 40/00
US. Cl. ...................... .. 705/36 R; 705/35; 705/36;
(58)
Field of Classi?cation Search ................ .. 705/36,
705/38
705/35, 38, 36 R See application ?le for complete search history.
References Cited U.S. PATENT DOCUMENTS 5,761,442 A *
6/1998
5,799,287 A
8/1998 Dembo
5,884,287 A * 6,003,018 A *
3/1999 12/1999
Barr et a1. .............. .. 705/36 R
1/2000 Maggioncalda et a1.
6,021,397 A
2/2000 Jones et al.
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beloW the value of a benchmark over a given time horizon, and a second value corresponding to an amount by Which the
value of the portfolio is expected to exceed the value of a benchmark over a given time horizon, in vieW of the range of different future scenarios. The invention provides a means
these tWo values, and to evaluate risk/reward performance measures using these tWo values Which can be used to rank
instruments, securities or portfolios. The invention also provides a means for pricing portfolio insurance for optimal
Rebane ...................... .. 705/36
705/36 R
Scott et a1. .. ..... .. 705/36 Baker ........................ .. 705/36
MARK-TO-MARKET
portfolio in terms of its performance relative to a speci?ed benchmark under a range of future scenarios. In particular, the invention takes a portfolio and calculates tWo values related to the portfolio: the ?rst value corresponding to an amount by Which the value of the portfolio is expected to fall
for determining the portfolio Which optimally trades-01f
Edesess .................. .. 705/36 R Michaud et a1. ........ .. 705/36 R
6,012,044 A
ABSTRACT
This invention relates to a system and method for valuing a
(2006.01)
(52)
(56)
(57)
portfolios. 27 Claims, 14 Drawing Sheets
MARK~TO~FUTURE
UPSIDE
6+): DOWNSIDE
US 7,171,385 B1 Page 2 OTHER PUBLICATIONS Dembo, Ron S. et al., Mark to future: A Comprehensive Guide to a
Revolution in the Evolution of Risk, Algorithmics, Nov. 1999. Dembo, Ron S. et al., 2000, “The Put/Call E?icient Frontier,” Algo
Research Quarterly 3(1), 13-25. Dembo, Ron et al., 1999, “The Practice of Portfolio Replication: A Practical Overview of Forward and Inverse Problems”, Annals of
Operations Research, 85: 267-284. Duf?e, D., 1996, Dynamic Asset Pricing Theory, Princeton Univer sity Press, Princeton, New Jersey, p. 3-19.
King, A.J., 1998, “Martingales and duality in contingent claims analysis: the discrete case,” Research Report, IBM Research Divi sion, TJ Watson Research Center, New York. MarkowitZ, H., 1952, “Portfolio Selection,” Journal of Finance, 7:
Saunders, David, Applications of Optimization to Mathematical Finance, Thesis; Graduate Department of Mathematics, University to Toronto, 1997.
Sharpe, W.F., 1998, “Morningstar’s Risk-Adjusted Ratings”, Finan cial Analysts Journal 54 (4) Jul/Aug. 21-33. Bernardo, Antonio E. and Olivier Ledoit, “Gain, Loss, and Asset Pricing”, The Journal of Political Economy: Feb. 2000; vol. 108, No. 1, pp. 144-172. Keating, Con and William F. Shadwick, “A Universal Performance
Measure”, The Finance Development Centre, London, Current Version: May 2002, pp. 1-41. Dembo, Ron S. et al. The Put/ Call E?icient Frontier, Algo Research Quarterly, Mar. 2000,vol. 3, No. 1. Dembo, Ron S. et al. Mark to Future: A Comprehensive Guide to a
77-91.
revolution in the evolution of Risk. Algorithmics Incorporated. Nov. 1999 (not released publicly before Nov. 26, 1999) 2.36 to 2.42.
Rosen, Dan et al., Scenario Optimization Approach to Pricing in Incomplete Markets, SIAM, Toronto, Jul. 14, 1998.
* cited by examiner
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T
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FOR EACH SCENARIO s V
FOR EACH INSTRUMENT I IN PORTFOLIO P
Ir DETERMINE VALUE(S) VFOR I, GIVEN S
SUM V's & STORE WITH PROBABILITY ASSOCIATED WITH s
OUTPUT DETERMINED SUMS AND ASSOCIATED PROBABILITIES
FIG. 3
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PROB
VALUE
FIG. 4
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SCENARIOS
N
T MtF TABLES
INSTRUMENTS
(TIME STEPS) 121
FIG. 5
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