Replicated derivatives having demand-based, adjustable returns, and trading exchange therefor

• US 20030236738A1
• Filed: 02/11/2003
• Published: 12/25/2003
• Est. Priority Date: 07/21/1999
• Status: Active Grant

• Current Assignee: Longitude LLC
• Original Assignee: Longitude LLC
• Inventors: Lange, Jeffrey, Harte, Marcus, Walden, Charles, Baron, Kenneth Charles
• Granted Patent: US 8,126,794 B2
• Time in Patent Office: Days
• US Class Current: 705/37
• CPC Class Codes: G06Q 30/08 Auctions
• 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
• CPC Class Codes: G07F 7/10 together with a coded signal , e.g. in the form of personal identification information, like personal identification number [PIN] or biometric data
• CPC Class Codes: H01L 21/28061 the conductor comprising a metal or metal silicide formed by deposition, e.g. sputter deposition, i.e. without a silicidation reaction H01L21/28052 takes precedence
• CPC Class Codes: H01L 29/4941 with a barrier layer between the silicon and the metal or metal silicide upper layer, e.g. Silicide/TiN/Polysilicon

Abstract

Methods and systems for trading and replicating contingent claims, such as derivatives strategies, in a demand-based auction are described. In one embodiment, a set of demand-based claims, each of which can be a vanilla option or a digital option, approximate or replicate the contingent claim into a vanilla replicating basis or a digital replicating basis, and the order for the contingent claim is then evaluated or processed in the demand-based auction. In another embodiment, a plurality of strikes and a plurality of replicating claims are established for a demand-based auction on an event, one or more replicating claims striking at each of the strikes in the auction. A contingent claim, such as a derivatives strategy, is replicated with a replication set that includes one or more of the replicating claims in the auction. The equilibrium price and/or the payout for the derivatives strategy is determined as a function of the demand-based valuation of each of the replicating claims in the replication set. For a customer order requesting a number of a certain derivatives strategy in the demand-based auction and a limit price per derivatives strategy, the premium of the customer order is determined as a product of the equilibrium price for the derivatives strategy and a filled number of derivatives strategies for the order, each determined as a function of the demand-based valuation of each of the replicating claims in the demand-based auction.

Claims

1. A method for trading contingent claims in a demand-based auction, comprising:

approximating a contingent claim with a set of demand-based claims, the demand-based claims including at least one vanilla option.

2. The method according to claim 1, wherein the approximating step includes the step of:

approximating the contingent claim with the set of demand-based claims, the demand-based claims also including at least one digital.

3. The method according to claim 1, wherein the approximating step includes the step of:

replicating the contingent claim with the set of demand-based claims.

4. The method according to claim 1, wherein the approximating step includes the step of:

approximating the contingent claim with the set of demand-based claims, the demand-based claims including at least one of a vanilla put and a vanilla call.

5. The method according to claim 1, wherein the approximating step includes the step of:

approximating the contingent claim with the set of demand-based claims, the demand-based claims including at least one of a resealed vanilla put knock out and a rescaled vanilla call knock out.

6. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a derivatives strategy.

7. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a structured instrument.

8. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a financial product.

9. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a digital call.

10. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a digital put.

11. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a range binary.

12. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a vanilla call.

13. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a vanilla put.

14. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a vanilla call spread.

15. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a vanilla put spread.

16. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a vanilla straddle.

17. The method according to claim 1, further including the, step of:

defining the contingent claim to be approximated as a collared vanilla straddle.

18. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a forward.

19. The method according to claim 1, further including the step of:

defining the contingent claim to be approximated as a collared forward.

20. A method for trading contingent claims in a demand-based auction on an event, comprising:

determining a value of a contingent claim as a function of a demand-based valuation of each vanilla option in a replication set for the contingent claim, the replication set including at least one vanilla option.

21. The method according to claim 20, wherein the determining step includes the step of:

determining an equilibrium price for each vanilla option in the replication set as a function of at least one parameter of the vanilla option and a total premium invested in the demand-based auction.

22. The method according to claim 21, further comprising the step of:

determining an equilibrium price for the contingent claim as a function of the equilibrium price of each vanilla option and a quantity of each vanilla option in the replication set.

23. The method according to claim 22, further comprising the step of:

accepting an order for a quantity of contingent claims.

24. The method according to claim 23, further comprising the step of:

determining a premium amount for the order as a function of the equilibrium price of the contingent claim and the quantity of filled contingent claims in the order.

25. The method according to claim 21, wherein the step of determining the equilibrium price for each vanilla option includes the step of:

determining a strike, a payout profile, and a quantity of each vanilla option in the replication set as a function of a payout profile of the contingent claim, the payout profile providing a payout as a function of strikes in the auction, the strikes corresponding to possible outcomes of the event.

26. The method according to claim 25, wherein the step of determining the equilibrium price for each vanilla option includes the step of:

determining the equilibrium price of each vanilla option in the replication set as a function of the strike, the payout profile, and the quantity of the vanilla option in the replication set, and a total amount invested in the demand-based auction.

27. The method according to claim 20, wherein the determining step includes the step of:

determining the value of the contingent claim as a function of a demand-based valuation of each vanilla option and digital option in the replication set for the contingent claim, the replicating set including at least one vanilla option and at least one digital option.

28. A method for conducting a demand-based auction on an event, comprising the steps of:

establishing a plurality of strikes for the auction, each strike corresponding to a possible outcome of the event;

establishing a plurality of replicating claims for the auction, at least one replicating claim striking at a strike in the plurality of strikes;

replicating a contingent claim with a replication set including at least one of the plurality of replicating claims; and

determining at least one of an equilibrium price and a payout for the contingent claim as a function of a demand-based valuation of each of the replicating claims in the replication set.

29. The method according to claim 28, wherein the step of establishing the plurality of strikes includes the step of:

corresponding each strike to a possible measurement of the event, a possible measurement being a possible outcome of the event.

30. The method according to claim 29, further comprising the step of:

selecting an event of economic significance for the auction, the event of economic significance being characterized with a minimum possible measurement and a maximum possible measurement as the event of the demand-based auction.

31. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with a finite quantity for the minimum possible measurement of the event.

32. The method according to claim 31, wherein the step of establishing the plurality of strikes, includes the step of:

establishing a first strike corresponding to the minimum possible measurement of the event.

33. The method according to claim 32, wherein the step of establishing the plurality of replicating claims includes the step of:

establishing a replicating rescaled vanilla put knock out as one of the replicating claims in the auction, the rescaled vanilla put knock out knocking out at one measurement unit below the first strike, and striking at a second strike, the second strike being at least two measurement units apart from the first strike.

34. The method according to claim 32, wherein the step of establishing the plurality of replicating claims includes the step of:

establishing a replicating rescaled vanilla call knock out as one of the replicating claims in the auction, the rescaled vanilla put knock out striking at the first strike, and knocking out at a second strike, the second strike being at least two measurement units apart from the first strike.

35. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with a finite quantity for the maximum possible measurement of the event.

36. The method according to claim 35, wherein the step of establishing the plurality of strikes, includes the step of:

establishing a last strike corresponding to the maximum possible measurement of the event.

37. The method according to claim 36, wherein the step of establishing the plurality of replicating claims, includes the step of:

establishing a replicating rescaled vanilla put knock out as one of the replicating claims in the auction, the rescaled vanilla put knock out striking at the last, strike, and knocking out at one measurement unit below a penultimate strike, the penultimate strike being at least two measurement units less than the last strike.

38. The method according to claim 36, wherein the step of establishing the plurality of replicating claims includes the step of:

establishing a replicating resealed vanilla call knock out as one of the replicating claims in the auction, the resealed vanilla put knock out knocking out at the last strike, and striking at a penultimate strike, the penultimate strike being at least two measurement units less than the last strike.

39. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with an infinite quantity for the minimum possible measurement of the event.

40. The method according to claim 39, wherein the step of establishing the plurality of strikes, includes the step of:

establishing a first strike at a finite possible measurement of the event above the minimum possible measurement.

41. The method according to claim 40, wherein the step of establishing the plurality of replicating claims includes the step of:

establishing a replicating digital put striking as one of the replicating claims in the auction, the replicating digital put striking at the first strike.

42. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with an infinite quantity for the maximum possible measurement of the event.

43. The method according to claim 42, wherein the step of establishing the plurality of strikes, includes the step of:

establishing a last strike at a finite possible measurement of the event below the maximum possible measurement of the event.

44. The method according to claim 43, wherein the step of establishing the plurality of replicating claims, includes the step of:

establishing a replicating digital call striking as one of the replicating claims in the auction, the replicating digital call striking at the last strike.

45. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with an unbounded minimum possible measurement, and an unbounded maximum possible measurement.

46. The method according to claim 45, wherein the step of establishing the plurality of strikes includes the steps of:

establishing a first strike at a finite possible measurement of the event above the unbounded minimum possible measurement of the event; and

establishing a last strike at a finite possible measurement of the event below the unbounded maximum possible measurement of the event.

47. The method according to claim 46, wherein the step of establishing the plurality of replicating claims includes the steps of:

establishing a digital put as a first replicating claim in the auction, the digital put striking at the first strike; and

establishing a digital call as a last replicating claim in the auction, the digital call striking at the last strike.

48. The method according to claim 47, wherein the step of establishing the plurality of replicating claims includes the step of:

establishing at least one replicating resealed vanilla call as an intermediate replicating claim in the auction, each replicating resealed vanilla call striking at a preceding strike and knocking out at a subsequent strike in the plurality of strikes in the auction.

49. The method according to claim 47, wherein the step of establishing the plurality of replicating claims includes the step of;

establishing at least one replicating rescaled vanilla put as an intermediate replicating claim in the auction, each replicating rescaled vanilla put striking at a subsequent strike, and knocking out at one measurement unit below a preceding strike, the possible measurement of the event corresponding to each preceding strike being at least two measurement units less than the possible measurement of the event corresponding to the subsequent strike.

50. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with a non-negative quantity as the minimum possible measurement of the event.

51. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with a negative quantity as the minimum possible measurement of the event.

52. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with a finite variance.

53. The method according to claim 30, wherein the selecting step includes the step of:

selecting the event characterized with an infinite variance.

54. The method according to claim 28, wherein the step of establishing the plurality of strikes includes the step of:

establishing each preceding strike at least one measurable unit apart from each subsequent strike in the plurality of strikes, each measurable unit corresponding to a measurable increment of the event.

55. The method according to claim 54, wherein the step of establishing each preceding strike at least one measurable unit apart from each subsequent strike, includes the step of:

establishing each preceding strike at one tick apart from each subsequent strike, each tick corresponding to the measurable unit of the event.

56. The method according to claim 55, wherein the step of establishing the plurality of replicating claims for the auction, includes the step of:

establishing a plurality of replicating digital options as the plurality of replicating claims in the auction.

57. The method according to claim 56, wherein the step of establishing the plurality of replicating digital options, includes the step of:

establishing at least one replicating digital range as at least one of the plurality of replicating digital options, each digital range striking at a preceding strike, and knocking out at subsequent strike in the auction.

58. The method according to claim 54, wherein the step of establishing each preceding strike at least one measurable unit apart from each subsequent strike, includes the step of:

establishing each preceding strike at least two measurable units apart from each subsequent strike in the plurality of strikes.

59. The method according to claim 58, wherein the step of establishing the plurality of replicating claims for the auction, includes the step of:

establishing at least one replicating vanilla option as at least one of the plurality of replicating claims in the auction.

60. The method according to claim 59, further comprising the step of:

offering a vanilla option as the contingent claim replicated with the replication set.

61. The method according to claim 59, further comprising the step of:

offering a digital option as the contingent claim replicated with the replication set.

62. The method according to claim 59, wherein the step of establishing the plurality of replicating claims for the auction, includes the step of:

establishing at least one replicating digital option as at least one of the plurality of replicating claims in the auction.

63. The method according to claim 62, further comprising the step of:

offering a vanilla option as the contingent claim replicated with the replication set.

64. The method according to claim 62, further comprising the step of

offering a digital option as the contingent claim replicated with the replication set.

65. The method according to claim 59, wherein the step of establishing at least one replicating vanilla option, includes the step of:

establishing a replicating resealed vanilla call knock out as one of the at least one replicating vanilla options, each replicating resealed vanilla call knock out striking at each preceding strike in the auction, and knocking out at each subsequent strike in the auction.

66. The method according to claim 59, wherein the step of establishing at least one replicating vanilla option, includes the step of:

establishing a replicating resealed vanilla put knock out as one of the at least one replicating vanilla options, each replicating vanilla put knock out knocking out at one measurement unit below each preceding strike, and striking at each subsequent strike in the auction.

67. The method according to claim 28, further comprising the step of:

determining a quantity of the replicating claims as a function of a quantity of strikes in the auction.

68. The method according to claim 28, further comprising the step of:

placing opening orders on each one of the replicating claims in the plurality of replicating claims in the auction.

69. The method according to claim 68, wherein the placing step includes the step of:

placing opening orders for equal amounts on each replicating claim.

70. The method according to claim 68, wherein the placing step includes the step of:

determining an amount for an opening order on a replicating claim as a function of an estimated value of the replicating claim.

71. The method according to claim 68, wherein the placing step includes the step of:

determining an amount for an opening order on a replicating claim as a function of an estimated equilibrium price of the replicating claim.

72. The method according to claim 28, further comprising the step of:

offering a derivatives strategy as the contingent claim.

73. The method according to claim 72, wherein the step of determining at least one of the equilibrium price and the payout for the contingent claim, includes the step of:

determining at least one of an equilibrium price and a payout for the derivatives strategy as a function of a demand-based valuation of each of the replicating claims in the replication set.

74. The method according to claim 73, wherein the replicating step, includes the step of:

replicating the derivatives strategy with a replication set including at least one of the plurality of replicating claims.

75. The method according to claim 74, wherein the replicating step includes the step of:

selecting at least one replicating claim for the replication set as a function of a payout profile of the derivatives strategy.

76. The method according to claim 75, further comprising the step of:

receiving an indication of the payout profile and a selected outcome for the derivatives strategy, the selected outcome corresponding to at least one of the plurality of strikes in the auction.

77. The method according to claim 76, further comprising the step of:

defining the payout profile of the derivatives strategy as providing a payout as a function of the selected outcome of the event, the function being a piecewise linear function.

78. The method according to claim 76, further comprising the step of:

defining the payout profile of the derivatives strategy as providing a payout as a function of the selected outcome of the event, the function being a non-linear function.

79. The method according to claim 76, further comprising the step of:

defining the payout profile of the derivatives strategy as providing a payout as a function of the selected outcome of the event, the function being a continuous function.

80. The method according to claim 79, wherein the replicating step includes the step of:

determining a quantity of each replicating claim in the replication set with an ordinary least squares regression analysis of a payout profile of the derivatives strategy.

81. The method according to claim 79, wherein the replicating step includes the step of:

determining a quantity of each replicating claim in the replication set with a weighted least squares analysis of a payout profile of the derivatives strategy.

82. The method according to claim 79, wherein the replicating step includes the step of:

determining a quantity of each replicating claim in the replication set with a regression analysis of a payout profile of the derivatives strategy.

83. The method according to claim 74, wherein the replicating step includes the step of:

determining a quantity of each replicating claim in the replication set as a function of a payout profile of the derivatives strategy.

84. The method according to claim 83, wherein the step of establishing a plurality of replicating claims, includes the step of:

establishing a plurality of replicating digital options as the plurality of replicating claims in the auction.

85. The method according to claim 74, wherein the step of establishing a plurality of replicating claims, includes the step of:

establishing at least one replicating vanilla option as at least one of the plurality of replicating claims in the auction.

86. The method according to claim 85, wherein the replicating step includes the step of:

determining a quantity of each replicating claim in the replication set as a function of a payout profile, a maximum payout and a minimum payout of the derivatives strategy.

87. The method according to claim 86, wherein the step of determining the quantity of replicating claims in the replication set includes the step of:

determining the maximum payout of the derivatives strategy as a maximum of a desired payout if an observed outcome of the event corresponds to a measurement within the plurality of strikes, a measurement below a lowest strike in the plurality of strikes, and a measurement above a highest strike in the plurality of strikes in the auction.

88. The method according to claim 86, wherein the step of determining the quantity of replicating claims in the replication set includes the step of:

determining the minimum payout of the derivatives strategy as a minimum of a desired payout if an observed outcome of the event corresponds to a measurement within the plurality of strikes, a measurement below a lowest strike in the plurality of strikes, and a measurement above a highest strike in the plurality of strikes in the auction.

89. The method according to claim 74, further comprising the step of:

determining a potential profit and loss associated with each replicating claim in the replication set, as a function of a payout profile of the derivatives strategy and a strike corresponding to a possible outcome of the event.

90. The method according to claim 74, further comprising the step of:

minimizing a potential maximum profit and loss associated with each replicating claim in the auction.

91. The method according to claim 74, further comprising the step of:

configuring an opening order in the auction that minimizes a potential maximum profit and loss associated with sponsoring the auction.

92. The method according to claim 74, wherein the step of establishing the plurality of replicating claims, includes the step of:

determining a type of each replicating claim as a function of a characteristic of the event to minimize a potential maximum profit and loss associated with sponsoring the auction.

93. The method according to claim 74, further comprising the step of:

determining at least one type of derivatives strategy to offer in the auction that minimizes a potential maximum profit and loss associated with sponsoring the auction.

94. The method according to claim 93, wherein the step of determining the at least one type of offered derivatives strategy, includes the step of:

offering derivatives strategies that have a payout profile providing at least one of an upper bound maximum payout and a lower bound minimum payout in order to reduce to zero a potential maximum profit and loss associated with replicating the derivatives strategy.

95. The method according to claim 74, further comprising the steps of:

offering a derivatives strategy having a payout profile with an unbounded minimum possible payout; and

determining a quantity of a first replicating claim in the replication set as a function of an expected value of the event, in order to minimize a potential maximum profit and loss associated with offering the derivatives strategy.

96. The method according to claim 74, further comprising the steps of:

offering a derivatives strategy having a payout profile with an unbounded maximum possible payout; and

determining a quantity of a last replicating claim in the replication set as a function of an expected value of the event, in order to minimize a potential maximum profit and loss associated with offering the;

derivatives strategy.

97. The method according to claim 92, wherein the step of determining the type of each replicating claim, includes the step of:

determining the type of each replicating claim as a function of a distance between the strikes in the plurality of strikes.

98. The method according to claim 92, wherein the step of determining the type of each replicating claim includes the step of:

determining the type of each replicating claim as a function of whether the event has one of a lower bound and an upper bound of possible outcomes.

99. The method according to claim 98, further including the step of:

selecting prices of a currency in units of another currency as the event for the auction.

100. The method according to claim 98, further including the step of:

selecting prices of a commodity as the event for the auction.

101. The method according to claim 98, further including the step of:

selecting prices of a fixed income instrument as the event for the auction.

102. The method according to claim 98, further including the step of:

selecting prices of an equity as the event for the auction.

103. The method according to claim 98, further including the step of:

selecting a number of heating degree days and cooling degree days over a set period as the event.

104. The method according to claim 103, further including the step of:

offering a weather derivative as the derivatives strategy tradable in the auction.

105. A method for processing a customer order including at least one of a derivatives strategy, in a demand-based auction on an event, the auction including at least one customer order, comprising the steps of:

establishing strikes for the auction, each one of the strikes corresponding to a possible outcome of the event;

establishing replicating claims for the auction, at least one replicating claim striking at one of the strikes;

replicating each derivatives strategy in the customer order with a replication set including at least one of the replicating claims in the auction; and

determining a premium for the customer order by engaging in a demand-based valuation of each one of the replicating claims in the replication set for each one of the derivatives strategies in the customer order.

106. The method according to claim 105, wherein the determining step includes the step of:

determining an equilibrium price for each one of the replicating claims in the auction, as a function of a payout profile and strike of the one of the replicating claim, and an equilibrium price, a payout profile and strike of each other replicating claim in the auction, and a total amount invested in the auction.

107. The method according to claim 106, wherein the step of determining the premium for the customer order, includes the step of:

determining a replication weight for each one of the replicating claims in the replication set for the derivatives strategy as a function of a payout profile and at least one selected strike of the derivatives strategy, each one of the at least one selected strike corresponding to a selected outcome of the event.

108. The method according to claim 107, wherein the step of determining the replication weight, includes the step of:

determining a quantity of each one of the replicating claims at each one of the strikes in the replication set to create a replicated payout profile for the replication set approximating the payout profile and the at least one selected strike of the derivatives strategy, the quantity of each one of the replicating claims being the replication weight for the one of the replicating claims.

109. The method according to claim 107, wherein the step of determining the premium for the customer order, includes the step of:

determining an equilibrium price for the derivatives strategy, by adding together a product of the equilibrium price of each respective one of the replicating, claims with the replication weight of the respective one of the replicating claims in the replication set for the derivatives strategy.

110. The method according to claim 109, wherein the step of determining the premium for the customer order, includes the step of:

multiplying the equilibrium price for the derivatives strategy with an equilibrium number of the derivatives strategy in the customer order.

111. The method according to claim 110, wherein the step of determining the premium for the customer order, includes the step of:

determining the total amount invested in the auction by summing up the premiums for the customer order, for each additional Customer order in the auction, and a premium for an opening order on all of the replicating claims in the auction.

112. The method according to claim 110, further comprising the step of:

specifying, for the customer order, a requested number of derivatives strategies, a limit price per derivatives strategy, a payout profile of the derivatives strategy, an order type as one of a purchase order and a sale order of derivatives strategies, and at least one selected strike for the derivatives strategy, each selected strike corresponding to at least one selected outcome of the event.

113. The method according to claim 112, further comprising the step of:

determining an equilibrium number of derivatives strategies for the customer order as a function of the requested number of derivatives strategies, the order type, and a relationship between the equilibrium price of the derivatives strategy, the limit price for the derivatives strategy, and the total amount invested in the auction.

114. The method according to claim 113, further comprising the step of:

filling the customer order with the requested number of derivatives strategies for the customer order, when the customer order is a purchase order and the equilibrium price of the derivatives strategy is one of less than and equal to the limit price for the derivatives strategy, the equilibrium number of derivatives strategies being equal to the requested number of derivatives strategies.

115. The method according to claim 113, further comprising the step of:

filling the customer order with the requested number of derivatives strategies for the customer order, when the customer order is a sale order and the equilibrium price of the derivatives strategy is one of greater than and equal to the limit price for the derivatives strategy, the equilibrium number of derivatives strategies being equal to the requested number of derivatives strategies.

116. The method according to claim 113, wherein the step of determining the equilibrium number of derivatives strategies for the customer order, includes the step of:

adjusting the limit price of the derivatives strategy with one of a minimum possible payout and a maximum possible payout for the derivatives strategy, as a function of the order type.

117. The method according to claim 113, wherein the step of determining the premium for the customer order, includes the step of:

performing an iteration by repeating the steps of determining, for each customer order in the auction, the equilibrium number of derivatives strategies in the customer order;

the equilibrium price of the derivatives strategy in the customer order, and the equilibrium price of each one of the replicating claims in the replication set for the derivatives strategy in the customer order, until reaching a maximization of the total amount invested in the auction.

118. The method according to claim 117, wherein the step of performing the iteration, includes the step of:

performing the iteration until satisfying a condition that the limit price specified for the derivatives strategy, in each one of the customer orders, restricts the determination of the equilibrium price for the derivatives strategy.

119. The method according to claim 117, wherein the step of performing the iteration, includes the step of:

performing the iteration until satisfying a condition that the equilibrium price for each of the replicating claims is positive.

120. The method according to claim 117, wherein the step of performing the iteration, includes the step of:

performing the iteration until satisfying a condition that the equilibrium prices for each one of the replicating claims in the auction sums up to one.

121. The method according to claim 117, wherein the step of performing the iteration, includes:

the step of;

performing the iteration until satisfying a condition that the total amount invested in the auction is equal to an aggregate filled amount in the auction.

122. The method according to claim 117, wherein the step of performing the iteration, includes the step of:

performing the iteration until satisfying a condition that, for any two of the replicating claims in the auction, a proportion of a total premium for a first of the two of the replicating claims to a total premium for a second of the two of the replicating claims equals a proportion of the equilibrium price of the first of the two of the replicating claims to the equilibrium price of the second of the two of the replicating claims in the auction.

123. The method according to claim 117, wherein the step of performing the iteration, includes the step of:

performing the iteration until satisfying a condition that a total premium for each one of the replicating claims in the auction is equal to an aggregate filled amount for the one of the replicating claims in the auction.

124. The method according to claim 123, further comprising the step of:

determining the aggregate filled amount for each one of the replicating, claims in the auction by summing up across all customer orders in the auction, the product of the replication weight for the one of the replicating claims for the derivatives strategy in each respective customer order, with the equilibrium number of derivatives strategies in the respective customer order.

125. The method according to claim 124, wherein the step of determining the aggregate filled amount for each one of the replicating claims in the auction, includes the step of:

adding to the sum across all customer orders, a filled amount for an opening order on the one of the replicating claims.

126. The method according to claim 125, wherein the adding step, includes the step of:

determining the filled amount for the opening order on the one of the replicating claims by dividing a premium, of the opening order with the equilibrium price of the one of the replicating claim.

127. The method according to claim 125, wherein step of performing the iteration, includes the step of:

performing the iteration by repeating the steps of;

determining, for each one of replicating claims in the auction, the aggregate filled amount for the one of the replicating claims; and

determining, for each one of the customer orders, the equilibrium number of derivatives strategies in the customer order, the equilibrium price of the derivatives strategy, and the equilibrium price of each one of the replicating claims in the replication set for the derivatives strategy in the customer order, until reaching the maximization of the total amount invested in the auction, and until satisfying the condition.

128. A method for investing in a demand-based auction on an event, comprising:

providing an indication of at least one selected strike and a payout profile for at least one derivatives strategy, each of the at least one selected strike corresponding to a selected outcome of the event, and each of the at least one selected strike being selected from a plurality of strikes established for the auction, each of the strikes corresponding to a possible outcome of the event;

receiving an indication of a price for each of the at least one derivatives strategy, the price being determined by engaging in a demand-based valuation of a replication set replicating the derivatives strategy, the replication set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at one of the strikes.

129. The method according to claim 128, further comprising the step of:

ordering the at least one derivatives strategy.

130. The method according to claim 128, wherein the receiving step;

includes the step of;

receiving the indication of the price for each of the at least one derivatives strategy, the price being determined by summing up a product of the equilibrium price of each one of the replicating claims in the replication set with a number of the one of the replicating claims in the replication set, the equilibrium price for each one of the replicating claims in the auction being determined as a function of a payout profile and strike of the one of the replicating claims, and an equilibrium price, a payout profile and strike of each other replicating claim in the auction, and a total amount invested in the auction.

131. The method according to claim 128, wherein the providing step includes the step of:

providing an indication of a limit price for each of the at least one derivatives strategy, and a requested number of the at least one derivatives strategy.

132. The method according to claim 131, wherein the receiving step includes the step of:

receiving an indication of a filled number of the at least one derivatives strategy, as a function of the requested number of the at least one derivatives strategy, the payout profile, the selected strikes and the limit price of each of the at least one derivatives strategy, and a total amount invested in the auction.

133. The method according to claim 132, wherein the step of receiving the indication of the price for each of the at, least one derivatives strategy, includes the step of:

receiving the indication of the price for each of the at least one derivatives strategy, the price by summing up a product of the equilibrium price of each one of the replicating claims in the replication set with a number of the one of the replicating claims in the replication set, the equilibrium price for each one of the replicating claims in the auction being determined as the function of a payout profile and strike of the one of the replicating claims, and an equilibrium price, a payout profile and strike of each other replicating claim in the auction, the limit price of the derivatives strategy, the filled number of the at least one derivatives strategy, and a total amount invested in the auction.

134. The method according to claim 133, wherein the step of receiving the indication of the price for each of the at least one derivatives strategy, the price being the sum of equilibrium prices of each one of the replicating claims in the replication set multiplied with the number of the one of the replicating claims in the replication set, includes the step of:

receiving the indication of the price for each of the at least one derivatives strategy, the price being the sum of equilibrium prices of each one of the replicating claims in the replication set multiplied with the number of the one of the replicating claims in the replication set, the number of each one of the replicating claims in the replication set being determined as a function of the payout profile of the derivatives strategy.

135. A computer system for processing a customer order including at least one of a derivatives strategy, in a demand-based auction on an event, the auction including at least one customer order, the computer system comprising:

at least one processor configured to;

establish strikes for the auction, each one of the strikes corresponding to a possible outcome of the event;

establish replicating claims for the auction, at least one replicating claim striking at one of the strikes; and

replicate each of the at least one derivatives strategy in the customer order with a replication set including at least one of the replicating claims in the auction; and

determine a premium for the customer order by engaging in a demand-based valuation of each one of the replicating claims in the replication set for each one of the at least one derivatives strategy in the customer order.

136. The computer system according to claim 135, further comprising:

at least one database module; and

at least one terminal, the processor being operative with the at least one database module and the at least one terminal.

137. The computer system according to claim 135, wherein the at least one processor includes a first processor and a second processor parallel to the first processor.

138. The computer system according to claim 137, wherein the first processor operates with the second processor, each processor configured to at least one of establish the strikes for the auction, establish the replicating claims for the auctions, replicate each of the at least one derivatives strategy with the replication set, and determine the premium for the customer order.

139. The computer system according to claim 137, wherein the first processor is configured to establish the strikes and the replicating claims for the auction, and the second processor is configured to replicate each one of the at least one derivatives strategy in the customer order with the replication set, and determine the premium for the customer order.

140. The method according to claim 136, further comprising:

a server housing the processor and the at least one database module; and

a network connecting the at least one database module and the processor with the at least one terminal.

141. A computer system for placing an order to invest in a demand-based auction on an event, the order including at least one derivatives strategy, the computer system comprising:

at least one processor configured to;

provide an indication of at least one selected strike and a payout profile for each derivatives strategy, each of the at least one selected strike corresponding to a selected outcome of the event, and each of the at least one selected strike being selected from a plurality of strikes established for the auction, each of the strikes corresponding to a possible outcome of the event;

receive an indication of a premium for the order, the premium of the order being determined by engaging in a demand-based valuation of a replication set replicating each one of the at least one derivatives strategy, the replication set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at one of the strikes.

142. The computer system according to claim 141, wherein the at least one processor is further configured to place the order.

143. The computer system according to claim 141, wherein the demand-based valuation of the replication set for each one of the at least one derivatives strategy in the customer order, includes a determination of equilibrium prices of each one of the replicating claims in the replication set as a function of a payout profile and strike of the one of the replicating claim, and an equilibrium price, a payout profile and strike of each other replicating claim in the auction, and a total amount invested in the auction.

144. The computer system according to claim 141, wherein the demand-based valuation of the replication set for each one of the at least one derivatives strategy in the customer order, includes a determination of a price for each of the at least one derivatives strategy as a sum of equilibrium prices of each one of the replicating claims in the replication set for the one of the derivatives strategy multiplied with a number of the one of the replicating claims in the replication set, the number of each one of the replicating claims in the replication set being determined as a function of the payout profile of the:

derivatives strategy.

145. The computer system according to claim 141, wherein the at least one processor is configured to receive an indication of a requested number of the at least one derivatives strategy in the customer order and a limit price for each of the at least one derivatives strategy.

146. The computer system according to claim 145, wherein the at least one processor is configured to receive an indication of a filled number of the at least one derivatives strategy in the customer order, the filled number of the at least one derivatives strategy being determined as a function of the requested number of the at least one derivatives strategy, the payout profile, the selected strikes and the limit price of each of the at least one derivatives strategy, and a total amount invested in the auction.

147. The computer system according to claim 146, wherein the at least one processor is configured to receive an indication of a price for each of the at least one derivatives strategy, the price being determined by summing up a product of the equilibrium price of each one of the replicating claims in the replication set for the derivatives strategy with a number of the one of the replicating claims in the replication set, the equilibrium price for each one of the replicating claims in the auction being determined as the function of a payout profile and strike of the one of the replicating claim, and an equilibrium price, a payout profile and strike of each other replicating claim in the auction, the limit price of the derivatives strategy, the filled number of the at least one derivatives strategy, and a total amount invested in the auction.

148. The computer system according to claim 147, wherein the number of each one of the replicating claims in the replication set for each of the at least one derivatives strategy is determined as a function of the payout profile of the derivatives strategy.

149. The computer system according to claim 147, wherein the at least one processor is configured to receive the indication of the premium for the customer order, the premium for the order being determined as a product of the filled number of the at least one derivatives strategy in the customer order with the price for the derivatives strategy.

150. The computer system according to claim 141, wherein the at least one processor is configured to receive the indication of the premium for the customer order prior to an occurrence of the event.

151. The computer system according to claim 141, wherein the at least one processor is configured to transmit the indication of the at least one selected strike and the payout profile for each of the at least one derivatives strategy to a server through an internet connection.

152. The computer system according to claim 141, wherein the at least one processor is configured to transmit the indication of the at least one selected strike and the payout profile for each of the at least one derivatives strategy to a server through a private network connection.

153. The computer system according to claim 141, wherein the at least one processor is configured to receive the indication of the premium for the order from a web site.

154. A method for executing a trade, comprising:

receiving a request for an order, the request indicating at least one selected strike and a payout profile for at least one derivatives strategy in the order, each of the at least one selected strike corresponding to a selected outcome of the event, and each of the at least one selected strike being selected from a plurality of strikes established for the auction, each of the strikes corresponding to a possible outcome of the event;

providing an indication of a premium for the order, the premium being determined by engaging in a demand-based valuation of a replication set replicating each of the at least one derivatives strategy in the order, the replication set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at one of the strikes; and

,

receiving an indication of a decision to place the order for the determined premium.

155. The method according to claim 154, further comprising the step of:

transmitting the indication of the premium for the order.

156. The method according to claim 154, wherein the step of receiving the request includes the step of:

receiving an indication of a limit price for each of the at least one derivatives strategy, and a requested number of the at least one derivatives strategy for the requested order.

157. A method for providing financial advice, comprising:

providing a person with advice about investing in at least one derivatives strategy in a demand-based auction, an order for the at least one of the derivatives strategy indicating at least one selected strike and a payout profile for at least one derivatives strategy in the order, each of the at least one selected strike corresponding to a selected outcome of the event, and each of the at least one selected strike being selected from a plurality of strikes established for the auction, each of the strikes corresponding to a possible outcome of the event,

wherein the premium for the order is determined by engaging in a demand-based valuation of a replication set replicating each of the at least one derivatives strategy in the order, the replication set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at one of the strikes.

158. A method of hedging, comprising:

determining an investment risk in at least one investment; and

offsetting the investment risk by taking a position in at least one derivatives strategy in a demand-based auction with an opposing risk, an order for the at least one derivatives strategy indicating at least one selected strike and a payout profile for the derivatives strategy in the order, each of the at least one selected strike corresponding to a selected outcome of the event, and each of the at least one selected strike being selected from a plurality of strikes established for the auction, each of the strikes corresponding to a possible outcome of the event,

wherein the premium for the order is determined by engaging in a demand-based valuation of a replication set replicating each of the at least one derivatives strategy in the order, the replication set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at one of the strikes.

159. The method according to claim 158, wherein the offsetting step includes the step of:

reducing a volatility of the at least one investment by taking the position in the at least one derivatives strategy in the demand-based auction with the opposing risk.

160. The method according to claim 159, wherein the reducing step includes the step of:

determining the position to be taking in the at least one derivatives strategy.

161. The method according to claim 160, wherein the reducing step includes the step of:

determining a volatility of a portfolio, the portfolio including the at least one investment and the at least one derivatives strategy.

162. A method of speculating, comprising:

determining an investment risk in at least one investment; and

increasing the investment risk by taking a position in at least one derivatives strategy in a demand-based auction with a similar risk, an order for the at least one derivatives strategy indicating at least one selected strike and a payout profile for at least one derivatives strategy in the order, each of the at least one selected strike corresponding to a selected outcome of the event, and each of the at least one selected strike being selected from a plurality of strikes established for the auction, each of the strikes corresponding to a possible outcome of the event, wherein the premium for the order is determined by engaging in a demand-based valuation of a replication set replicating each of the at least one derivatives strategy in the order, the replication set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at one of the strikes.

163. The method according to claim 162, wherein the increasing step includes the step of:

increasing a volatility of the at least one investment by taking the position in the at least one derivatives strategy in the demand-based auction with the similar risk.

164. The method according to claim 163 wherein the increasing step includes the step of:

determining the position to be taking in the at least one derivatives strategy.

165. The method according to claim 164, wherein the increasing step includes the step of:

determining a volatility of a portfolio, the portfolio including the at least one investment and the at least one derivatives strategy.

166. A computer program product capable of processing a customer order including at least one of a derivatives strategy, in a demand-based auction including at least one customer order, the computer program product comprising a computer usable medium having computer readable program code embodied in the medium for causing a computer to:

establish strikes for the auction, each one of the strikes corresponding to a possible outcome of the event;

establish replicating claims for the auction, at least one replicating claim striking at one of the strikes; and

replicate each one of the at least one derivatives strategy in the customer order with a replication set including at least one of the replicating claims in the auction; and

determine a premium for the customer order by engaging in a demand-based valuation of each one of the replicating claims in the replication set for each one of the derivatives strategies.

167. An article of manufacture comprising an information storage medium encoded with a computer-readable data structure adapted for use in placing a customer order in a demand-based auction over the Internet, the auction including at least one customer order, said data structure comprising:

at least one data field with information identifying at least one selected strike and a payout profile for each of the at least one derivatives strategy in the customer order, each of the at least one selected strike corresponding to a selected outcome of the event, and each of the at least one selected strike being selected from a plurality of strikes established for the auction, each of the strikes corresponding to a possible outcome of the event; and

at least one data field with information identifying a premium for the order, the premium being determined as a result of a demand-based valuation of a replication set replicating each of the at least one derivatives strategy in the order, the replication set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at one of the strikes.

168. A derivatives strategy for a demand-based market, comprising:

a first designation of at least one selected strike for the derivatives strategy, each of the at least one selected strike being selected from a plurality of strikes established for auction, each of the strikes corresponding to a possible outcome of the event;

a second designation of a payout profile for the derivatives strategy; and

a price for the derivatives strategy, the price being determined by engaging in a demand-based valuation of a replication set replicating the first designation and the second designation of the derivatives strategy, the replication set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at each one of the strikes.

169. An investment vehicle for a demand-based auction, comprising:

a demand-based derivatives strategy providing investment capital to the auction, an amount of the provided investment capital being dependent upon a demand-based valuation of a replication set replicating the derivatives strategy, the replicating set including at least one replicating claim from a plurality of replicating claims established for the auction, at least one of each of the replicating claims in the auction striking at one of the strikes.

170. The investment vehicle according to claim 169, wherein the demand-based derivatives strategy provides a predetermined payout according to a payout profile of the derivatives strategy, if one of the at least one selected strike corresponds to an observed outcome of the event.

171. The investment vehicle according to claim 169, wherein the demand-based derivatives strategy is allocated a loss of the investment capital if a strike corresponding to an observed outcome of the event is excluded from the at least one selected strikes for the derivatives strategy.

172. An article of manufacture comprising a propagated signal adapted for use in the performance of a method for trading a customer order including at least one of a derivatives strategy, in a demand-based auction including at least one customer order,

a. the method comprising the steps of:

establishing strikes for the auction, each one of the strikes corresponding to a possible outcome of the event;

establishing replicating claims for the auction, at least one replicating claim striking at one of the strikes;

replicating each one of the at least one derivatives strategy in the customer order with a replication set including at least one of the replicating claims in the auction; and

determining a premium for the customer order by engaging in a demand-based valuation of each one of the replicating claims in the replication set for the derivatives strategy in the customer order.

b. the signal encoded with machine-readable information relating to a trade.

173. The article of manufacture according to claim 172, Wherein the information includes information relating to at least one selected strike for the customer order.

174. The article of manufacture according to claim 172, wherein the information includes information relating to a payout profile for each one of the derivatives strategies.

175. The article of manufacture according to claim 172, wherein the information includes information relating to the event.

176. The article of manufacture according to claim 172, wherein the information includes information relating to each of the at least one possible outcome.

177. The article of manufacture according to claim 172, wherein the information includes information relating to each of the at least one replicating claim in the auction.

178. The article of manufacture according to claim 172, wherein the information includes information relating to the replication set for each derivatives strategy.

179. The article of manufacture according to claim 172, wherein the information includes information relating to an identity of a trader.

180. The article of manufacture according to claim 172, wherein information includes information relating to an execution of the trade.

181. A computer system for conducting demand-based auctions on an event, comprising:

at least one user interface processor configured to communicate with a plurality of terminals which are adapted to enter demand-based order data for an auction;

a database unit configured to maintain an auction information database;

an auction processor configured to process at least one demand-based auction and to communicate with the user interface processor and the database unit, wherein the auction processor is configured to generate auction transaction data based on auction order data received from the user interface processor and to send the auction transaction data for storing to the database unit, and wherein the auction processor is further configured to establish a plurality of strikes for the auction, each strike corresponding to a possible outcome of the event, to establish a plurality of replicating claims for the auction, at least one replicating claim striking at a strike in the plurality of strikes, to replicate a contingent claim with a replication set including at least one of the plurality of replicating claims, and to send the replication set for storing to the database unit; and

a calculation engine configured to determine at least one of an equilibrium price and a payout for the contingent claim as a function of a demand-based valuation of each of the replicating claims in the replication set stored in the database unit.

182. The computer system according to claim 181, wherein the auction processor is configured to maintain an auction state for the auction and to process auction order data received from the user interface processor depending on the state of the auction.

183. The computer system according to claim 182, wherein the auction processor is configured to notify the calculation engine when new transaction data has been generated and stored in the database unit.

184. The computer system according to claim 183, wherein the calculation engine is configured to recalculate at least one of the equilibrium price and the payout for the contingent claim when a notification of a new transaction is received.

185. The computer system according to claim 181, which is configured to verify that calculated auction trading data meet predetermined constrains.

186. The computer system according to claim 181, comprising a limit order book processor configured to accept limit order book requests for an auction from the user interface processor.

187. The computer system according to claim 186, comprising a limit order book engine configured to communicate with the limit order book processor and to calculate limit order book prices.

188. The computer system according to claim 187, wherein the limit order book engine is configured to communicate with the calculation engine in order to receive the equilibrium price and to calculate limit order book prices responsive to the received equilibrium price.