NON-BIASED, CENTRALLY-CLEARED FINANCIAL INSTRUMENT AND METHOD OF CLEARING AND SETTLING

Abstract

In accordance with the principles of the present invention a non-biased, computer-implemented financial instrument electronic trading system and electronic central clearinghouse are provided. The electronic trading system and electronic central clearinghouse operate to provide electronic trading of financial instruments that are non-biased in that the electronic trading system and electronic clearing house address at least one of two effects that result from the difference between variation margin on a cleared financial instrument and collateral posted on an uncleared financial instrument, the first effect being a systematic advantage of being short the financial instrument when there is a correlation between the value of the financial instrument and interest rates, referred to as a convexity bias, and the second effect being a distortion in the financial instrument when an underlying asset value of the financial instrument changes, referred to as a net present value (NPV) effect.

Claims

1-44. (canceled)

45. A computer-implemented financial instrument electronic trading platform in communication with an electronic central clearinghouse, said system including; a memory of an electronic trading platform that receives an identity of a first party, an identity of a first financial instrument, a buy/sell request, an identity of a second party, an identity of a second financial instrument, and a sell/buy request; a processor in communication with memory of the electronic trading platform electronically that automatically determines if the first financial instrument matches the second financial instrument; if the first financial instrument matches the second financial instrument, then a processor in communication with memory of the electronic trading platform electronically automatically determines if the buy/sell request matches the sell/buy request; and if the buy/sell request matches the sell/buy request the created, centrally cleared, and settled financial instrument contains at least one of two effects that result from the difference between variation margin on a cleared financial instrument and collateral posted on an uncleared financial instrument, the first effect being a systematic advantage of being short the financial instrument when there is a correlation between the value of the financial instrument and interest rates, referred to as a convexity bias and the second effect being a distortion in the financial instrument when an underlying asset value of the financial instrument change, referred to as a net present value (NPV) effect, the improvement comprising: if the buy/sell request matches the sell/buy request, a processor in communication with memory of the electronic trading platform electronically automatically determines what a final settlement value of a financial instrument would be upon its stated expiration in accordance with: net accumulated value of cash flow—total return on variation margin for the life of the financial instrument; where, net accumulated value of cash flow is the accumulated value that the first party of the financial instrument receives minus the payments the first party makes, reinvested at the overnight rate from the date that the cash flow occurs to expiration of the financial instrument; total return on variation margin for the life of the financial instrument is the sum of the interest earned on the cumulative variation margin for each day reinvested at the overnight rate to expiration of the financial instrument; and the overnight rate is the rate specified by the exchange or clearinghouse to reflect the short-term financing rate of market participants; automatically electronically storing the final settlement value of the financial instrument upon its stated expiration in memory of the electronic central clearinghouse: and by a processor in communication with said memory of the electronic central clearinghouse centrally clearing and settling the financial instrument by automatically electronically associating the centrally cleared and settled financial instrument with a trading account associated with the first party and automatically electronically associating the centrally cleared and settled financial instrument with a trading account associated with the second party.

46. The computer-implemented financial instrument electronic trading system of claim 45 wherein the financial instrument is one of interest-rate swaps and interest-rate swap futures.

47. The computer-implemented financial instrument electronic trading system of claim 45 wherein the financial instrument is one of credit-default swaps and credit-default swap futures.

48. The computer-implemented financial instrument electronic trading system of claim 45 wherein the financial instrument is one of forward rate agreements and other interest-rate futures.

49. The computer-implemented financial instrument electronic trading system of claim 45 wherein the financial instrument is commodity swaps.

50. The computer-implemented financial instrument electronic trading system of claim 45 wherein the financial instrument is one of total return swaps and total return swap futures.

51. The computer-implemented financial instrument electronic trading system of claim 45 wherein the financial instrument is one of variance swaps and variance-swap futures.

52. The computer-implemented financial instrument electronic trading system of claim 45 wherein the financial instrument is one of cross-currency swaps and cross-currency swap futures.

53. The computer-implemented financial instrument electronic trading system of claim 45 wherein the financial instrument is one of foreign-exchange swaps and foreign exchange swap futures.

Description

BRIEF DESCRIPTION OF THE DRAWING

[0039] FIG. 1 is a flow-chart setting forth an example for determining the net accumulated value of cash flows for a terminal value of a non-biased, centrally-cleared financial instrument of the present invention.

[0040] FIG. 2 is a flow-chart setting forth an alternative example for determining the terminal value of a non-biased, centrally-cleared financial instrument of the present invention.

[0041] FIG. 3 is a non-limiting example of a hardware infrastructure that can be used to run a system that implements electronic clearing and settling of the non-biased, centrally-cleared financial instrument of the present invention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

[0042] While an exemplary embodiment of the invention illustrated and described has been built to trade on Eris Exchange, it will be appreciated that the present invention is not so limited and can be cleared on any clearinghouse, traded on other exchanges or trading platforms, regardless of whether located in the United States or abroad, traded through a private negotiation, traded in currencies other than United States dollars or traded as a future or as a cleared swap or other type of financial instrument. When used herein, the terms exchange and trading platform refer broadly to a marketplace in which securities, commodities, derivatives and other financial instruments are traded, and includes but is not necessarily limited to designated contract markets, exempt boards of trade, designated clearing organizations, securities exchanges, swap execution facilities, electronic communications networks, and the like.

[0043] As previously detailed, given the differences in the manner in which collateral is treated in uncleared financial instruments on the one hand and centrally-cleared financial instruments on the other hand, a centrally-cleared swap that is subject to the convexity bias and/or the NPV effect, whether traded as a future or otherwise, will, unless addressed, trade at a different value than the same swap that is uncleared. This could significantly impair the migration of swaps and other financial instruments that have traditionally not been cleared, particularly interest-rate swaps, to central clearing. The present invention provides a financial instrument that is economically equivalent to uncleared financial instruments, including swaps, thus facilitating the migration of uncleared financial instruments to centralized exchanges and/or to central clearing.

[0044] In accordance with the principles of the present invention, a centrally-cleared financial instrument is provided that addresses the convexity bias and the NPV effect. The non-biased, centrally-cleared financial instrument of the present invention is to be centrally cleared and can be traded either on or off an exchange or trading platform, whether traded as a future or other type of financial instrument. When used herein, non-biased refers to addressing the convexity bias or the NPV effect or both. The financial instruments to which the present invention applies include, but are not limited to, interest-rate swaps, interest-rate swap futures, credit default swaps, credit default swap futures, other interest-rate futures, FRAs, commodity swaps, and foreign-exchange swaps, regardless of the currency in which the financial instrument is denominated.

[0045] As the convexity bias arises from the correlation between the value of the cleared. financial instrument and fixed-income instruments in general, a non-biased, centrally-cleared financial instrument of the present invention defines its terminal value (i.e. the final settlement value of the financial instrument upon its stated expiration) in a way that offsets the co-movement of variation margin and the investment return on the variation margin during the life of the financial instrument. In one embodiment in accordance with the principles of the present invention, the non-biased, centrally-cleared financial instrument is a swap that defines its terminal value to be the net accumulated value of the payments of the swap, minus the accumulated value of interest on variation margin over the life of the swap. The accumulated value of payments includes coupon payments and compounded interest earned on coupon payments. When used herein, the term swap is used in a broad, functional sense, and is not meant to be limited to any particular regulatory or legal definition thereof.

[0046] In the example of an interest-rate swap, if interest rates increase, all else being constant, the yield on the interest-rate swap will go up, or, in the alternative, if the interest-rate swap is traded in price terms, the price of the interest-rate swap will go down. Assuming this interest-rate swap is centrally cleared and traded in price terms, a short position will have a positive cash flow from the variation margin when interest rates increase. Unless the convexity bias is addressed, the party holding the short position will be able to invest the variation margin for a higher return as a result of the correlation between the interest-rate swap and interest rates in general. In this case, a non-biased, centrally-cleared financial instrument of the present invention will adjust the final payment of the financial instrument to account for the convexity bias and make the cleared financial instrument of the present invention equivalent in economic terms to an uncleared interest-rate swap.

[0047] Subtracting the accumulated value of interest on variation margin from the terminal value of a financial instrument of the present invention addresses the NPV effect. Assume the expected net cash flow of a swap increases due to a change in the value of the underlying asset, rate, commodity or index. Without the adjustment, the proper marked-to-market value of a cleared swap will increase by an amount equal to the sum of the expected change in the future cash flows. In the case of a cleared swap, this amount is paid to the buyer at the end of the day through variation margin. A non-biased, centrally-cleared financial instrument of the present invention decreases the terminal value of the financial instrument by an amount equal to the total interest earned on the accumulated variation margin over the life of the financial instrument, negating the NPV effect. Furthermore, setting the convexity bias aside, a non-biased, centrally-cleared financial instrument of the present invention will have a change in its fair value equal to the change in the sum of the present value of the expected future cash flows, which coincides with the profit (loss) of an uncleared swap position.

[0048] When a swap is traded, regardless of whether it is an exchange-traded swap future, a cleared swap or a traditional, uncleared swap, all of the terms of the fixed and floating payments are agreed upon at the time the trade is consummated. When the financial instrument is an exchange-traded swap future or a centrally-cleared swap, the position is marked to market periodically, most commonly daily, and variation margin flows based on the marked-to-market settlement. In one embodiment, the terminal value of a non-biased, centrally-cleared financial instrument of the present invention can be determined as follows:

terminal value=net accumulated value of cash flows−total return on variation margin;

[0049] where, [0050] net accumulated value of cash flows is the accumulated value that a buyer (seller) of a financial instrument receives minus the payments the buyer (seller) makes, reinvested at the overnight rate from the date that the cash flow occurs to expiration of the financial instrument; [0051] total return on variation margin is the sum of the interest earned on the cumulative variation margin for each day reinvested at the overnight rate to expiration of the financial instrument; and [0052] the overnight rate is the rate specified by the exchange or clearinghouse to reflect the short-term financing rate of market participants.

[0053] The net accumulation of cash flows reinvested at the overnight rate over the life of the non-biased, centrally-cleared financial instrument of the present invention is necessary to make the financial instrument of the present invention equivalent to an uncleared financial instrument with similar terms. A party who enters into an uncleared interest-rate swap is able to invest cash received from the coupon payments daily at the overnight rate. When the party is obligated to make coupon payments under such a swap, the party will pay interest on any funds borrowed to make such payments or forego earning interest. The inclusion of the net accumulated value of cash flows in the definition of terminal value of the non-biased, centrally-cleared financial instrument of the present invention replicates the cash flows associated with the uncleared financial instrument.

[0054] The other component of the definition of the terminal value of the non-biased, centrally-cleared financial instrument of the present invention is the total return on variation margin. This adjustment addresses both the convexity bias and the NPV effect in a cleared financial instrument. While the adjustment achieves the same effect as LCH.Clearnet's Price Alignment Interest (PAI) by building the value into the final settlement price without managing the PAI cash flow on a daily basis, the current systems used to process traditional futures and cleared financial instruments will not need to change in order to handle a financial instrument created under the principles of the present invention. The PAI requires daily cash adjustments that the current systems for processing futures cannot handle. The present invention is superior in that regard and will facilitate the migration of uncleared swaps and other uncleared financial instruments to central clearing and to centralized marketplaces.

[0055] In another embodiment in accordance with the present invention, a constant can be added or subtracted to the above terminal value definition. Adding or subtracting a constant to the above terminal value definition may sometimes be preferable in order to be consistent with certain market conventions. Generally the profit and loss of a cleared financial instrument comes only from the price change, and, thus, modifying the price process by a constant does not change the nature of the financial instrument.

[0056] Referring to FIG. 1, a flow-chart of an example embodiment for determining the net accumulated value of cash flows for the terminal value of a non-biased, centrally-cleared financial instrument of the present invention is seen. In the case of an interest-rate swap, the non-biased, centrally-cleared financial instrument of the present invention would have the fixed rate as its coupon, and the term of the swap defines its expiration. Taking into account these factors, the net accumulated value of cash flows can specifically be determined as follows:

[00001]$\mathrm{net}\mathrm{accumulated}\mathrm{value}\mathrm{of}\mathrm{cash}\mathrm{flows}=\underset{i=1}{\overset{N}{.Math.}}{C}_{i}B\left(t_{c,i},T\right)-\underset{i=1}{\overset{M}{.Math.}}{L}_{i}B\left(t_{l,i},T\right)$

[0057] where, [0058] C.sub.i is the amount of fixed leg payment payable at time t.sub.c,j; [0059] L.sub.i is the amount of the floating leg payment payable at time t.sub.i,j; [0060] T is the expiration of the financial instrument; and [0061] B(t, T) is the value of the money market account at time T with an initial deposit of 1 at time t and accumulated at overnight rate.

[0062] And total return on variation margin can be determined as:

[00002]$\mathrm{total}\mathrm{return}\mathrm{on}\mathrm{variation}\mathrm{margin}=\underset{t=1}{\overset{T-1}{.Math.}}{P}_t{R}_{t}B\left(t+1,T\right),$

[0063] where [0064] P.sub.t is the settlement price of the financial instrument on day t, and [0065] R.sub.t is the overnight interest rate on day t.
Here we assume, without loss of generality, the initial trading price is zero.

[0066] Referring to FIG. 2, a flow-chart of an alternative example embodiment for determining the terminal value of a non-biased, centrally-cleared financial instrument of the present invention is seen. In this alternative determination of the terminal value, which is equivalent to the embodiments above, the terminal value can be determined as follows:

terminal value=net summation of cash flows−total return on modified variation margin,

[0067] where, using the previous notations,

[00003]$$\begin{gathered} \mathrm{net}\mathrm{summation}\mathrm{of}\mathrm{cash}\mathrm{flows}=\underset{i=1}{\overset{N}{.Math.}}{C}_i-\underset{i=1}{\overset{M}{.Math.}}{L}_i;\mathrm{and} \\ \mathrm{total}\mathrm{return}\mathrm{on}\mathrm{modified}\mathrm{variation}\mathrm{margin}=\underset{t=1}{\overset{T-1}{.Math.}}\left(P_t-\left(\text{?}{C}_i-\text{?}{L}_i\right)\right)R_{t}B\left(t+1,T\right).\text{?}\text{indicates text missing or illegible when filed} \end{gathered}$$

[0068] By rearranging the terms of the second terminal value definition, the equivalence of the two alternative definitions discussed above can be seen:

[00004]$\underset{i=1}{\overset{N}{.Math.}}{C}_i-\underset{i=1}{\overset{M}{.Math.}}{L}_i-\underset{t=1}{\overset{T-1}{.Math.}}\left(P_t-\left(\text{?}{C}_t-\text{?}{L}_i\right)\right)R_{t}B\left(t+1,T\right)=\left(\underset{i=1}{\overset{N}{.Math.}}{C}_i+\underset{i=1}{\overset{T}{.Math.}}\text{?}{C}_i{R}_{t}B\left(t+1,T\right)\right)\left(\underset{i=1}{\overset{M}{.Math.}}{L}_i+\underset{t=1}{\overset{T}{.Math.}}\text{?}{L}_i{R}_{t}B\left(t+1,T\right)\right)-\underset{t=1}{\overset{T}{.Math.}}{P}_t{R}_{t}B\left(t+1,T\right)=\underset{i=1}{\overset{N}{.Math.}}{C}_i\left(1+\text{?}{R}_{t}B\left(t+1,T\right)\right)-\underset{i=1}{\overset{M}{.Math.}}{L}_i\left(1+\text{?}{R}_{t}B\left(t+1,T\right)\right)-\underset{t=1}{\overset{T}{.Math.}}{P}_t{R}_{t}B\left(t+1,T\right)=\underset{i=1}{\overset{N}{.Math.}}{C}_{i}B\left(t_{c,i},T\right)-\underset{i=1}{\overset{M}{.Math.}}{L}_{i}B\left(t_{l,i},T\right)-\underset{t=1}{\overset{T}{.Math.}}{P}_t{R}_{t}B\left(t+1,T\right).\text{?}\text{indicates text missing or illegible when filed}$

[0069] The following are non-limiting examples of non-biased, centrally-cleared financial instruments created by adjusting the terminal value for the interest on variation margin in accordance with the principles of the present invention. In each example, the overnight rate is assumed to be equal to the yield on the applicable day. The discussion and the Tables set forth below are from the perspective of the buyer of the financial instrument unless otherwise noted.

EXAMPLE 1

[0070] This example shows that a non-biased, centrally-cleared financial instrument in accordance with the present invention can replicate the profit and loss of a spot-starting, uncleared interest-rate swap each day. Consider a 10-year OTC swap with $100 M notional value with a par coupon of 2.0%. The buyer will receive 2.0% semi-annual interest payments on the notional amount and pay 3-month LIBOR interest payments on the notional amount quarterly.

[0071] A non-biased, centrally-cleared financial instrument in accordance with the present invention can be created to replicate such a swap. This non-biased, centrally-cleared swap has a 2.0% coupon, 10 years to maturity. Suppose the yield changes to 2.1% on day 2. The following Table 1 compares the performance of an uncleared, interest-rate swap and a non-biased, centrally-cleared swap position for the first few days:

TABLE-US-00001 TABLE 1 Performance of an Uncleared Swap and a Non=Biased Swap Uncleared Swap Non-Biased, Centrally-Cleared Swap Total P&L Return on Total P&L Date Yield to Date* Value** Variation Margin**** to Date*** 1 2.0 0 0 0 0 2 2.1 −906,497 −906,497 0 −906,497 3 2.1 −906,550 −906,497 −53 −906,550 4 2.1 −906,603 −906,497 −53 −906,603 *The total profit and loss to date is computed as the net present value of the remaining cash flows; therefore, the value may change each day as the expiration date approaches even as the yield does not change. **Value refers to a proper settlement value of the non-biased, centrally cleared swap. ***The total profit and loss to date for a cleared swap is the change in the settlement value of that day plus the accumulated variation margin and compounded interest earned on the accumulated variation margin. ****The return on the variation margin is computed as the one day financing cost on the accumulated variation margin from the previous settlement.
Table 1 shows that the total profit and loss to date of an uncleared swap and that of a non-biased, centrally-cleared swap created pursuant to the principles of the present invention are identical each day.

EXAMPLE 2

[0072] This example shows that a non-biased, centrally-cleared financial instrument in accordance with the present invention can replicate the profit and loss of a seasoned, uncleared interest-rate swap. The coupon of a seasoned interest-rate swap is usually different from the par swap rate when the seasoned swap is traded; to compensate for this, an upfront payment is often made with the amount equal to the present value of the seasoned swap. As seen in Example 1, the buyer of the 2.0% coupon, spot-starting swap has a marked-to-market loss of $906,603 on day 4 after the yield changed to 2.1%. If the buyer decides to sell the swap on day 4, a loss of $906,603 is incurred, whether the trade is an uncleared swap or a non-biased, centrally-cleared swap future of the present invention. The following Table 2 shows the cash flow and profit and loss of the buyer of this seasoned swap:

TABLE-US-00002 TABLE 2 Cash Flew and Profit And Loss of Buyer of Seasoned Swap Non-Biased, Centrally-Cleared Swap Future Uncleared Swap Return Marked-to Return Total on Total Market Cash on Cash P&L to Variation P&L to Date Yield Value Flow* Flow** Date Value Margin Date 4 2.1 −906,603 906,603 0 0 −906,497 0 0 5 2.1 −906,655 0 53 0 −906,497 0 0 6 2.1 −906,708 0 53 0 −906,497 0 0 *Since the present value of the seasoned swap is negative on day 4, the buyer receives a payment equal to the present value, $906,603. **The initial payment generates interest income for the buyer each day.
Table 2 shows that the total profit and loss to date of a seasoned, uncleared swap can be replicated by a non-biased, centrally-cleared swap future created pursuant to the principles of the present invention, if the non-biased, centrally-cleared swap is initiated on the same day as the uncleared swap.

EXAMPLE 3

[0073] This example shows that a non-biased, centrally-cleared financial instrument in accordance with the present invention can replicate the profit and loss of an uncleared forward-starting interest-rate swap. Consider the same swap as specified in Example 1—a 10-year swap with $100 M notional value with the par. coupon 2.0%. In this example, the swap starting date is one year from the date it is traded. A non-biased, centrally-cleared swap future of the present invention is traded on the same day. Suppose after 6 months, the yield changes to 2.1. The following Table 3 shows the cash flow and profit and loss before and after the yield changes:

TABLE-US-00003 TABLE 3 Cash Flow and P&L Before and After Yield Change Uncleared Swap Non-Biased, Centrally-Cleared Swap Total P&L Return on Total P&L Date Yield to Date Value Variation Margin to Date 180 2.0 0 0 0 0 181 2.1 −897,081 −897,082 0 −897,081 182 2.1 −897,133 −897,081 −52 −897,133
Table 3 shows that the total profit and loss to date of a forward-starting, uncleared swap can be replicated by a non-biased, centrally-cleared swap future created pursuant to the principles of the present invention each day.

EXAMPLE 4

[0074] This example compares the economics of a centrally-cleared, interest-rate swap without adjustments for the convexity bias and the NPV Effect (referred to as an unadjusted cleared swap), with a non-biased, centrally-cleared swap in accordance with the present invention. The unadjusted cleared swap is assumed to be settled at the proper value each day. Continuing the example set forth in Example 1, when an uncleared swap trades at a yield of 2.0%, a convexity-biased, interest-rate swap future would trade at a higher yield. Assuming the convexity bias for a 10-year swap is 25 basis points, the equivalent par coupon of the interest-rate swap future without adjustment for the convexity bias is 2.25%. Table 4 compares the profit and loss of a non-biased, centrally-cleared swap future of the present invention and an unadjusted cleared swap:

TABLE-US-00004 TABLE 4 Profit and Loss after a Yield Change Non-Biased, Centrally- Cleared Swap Future Unadjusted Cleared Swap Coupon = 2 Coupon = 2.25 Return Return on Total on variation P&L to variation Total P&L Date Yield Value margin Date Value margin to Date 1 2.0 0 0 0 0 0 0 2 2.1 −906,497 0 −906,497  −1,000,000* 0 −1,000,000 3 2.1 −906,497 −53 −906,550 −1,000,000 −54 −1,000,054 *The fair settlement value is equal to the sum of the future cash flows.
Table 4 shows that the total profit and loss to date of a non-biased, centrally-cleared swap future created pursuant to the principles of the present invention is different from that of an unadjusted cleared swap due to the NPV effect. Furthermore, an unadjusted cleared swap is traded at a different par coupon from the uncleared swap due to the convexity bias.

EXAMPLE 5

[0075] This example shows non-biased swap future in accordance with the present invention can replicate the profit and loss of an off-market swap. An off-market swap is a swap that has a value other than zero at initiation. When an off-market swap is traded, the coupon is usually set to be higher or lower than the par swap rate, and an upfront payment is made between the parties.

[0076] Assume a $100M notional value, 10-year, uncleared spot-starting swap is traded when the par yield is 2.0% and the coupon is set to be 3.0%. The present value of this swap is $8,927,737. The corresponding non-biased, centrally-cleared swap future of the present invention is traded with the same terms. Table 5 shows that the non-biased, centrally-cleared swap future of the present invention replicates the profit and loss of this off-market, uncleared swap when the yield changes to 2.1%:

TABLE-US-00005 TABLE 5 Cash Flow and Profit and Loss of an Off-Market Swap Non-Biased, Centrally-Cleared Uncleared Swap Swap Future Marked- Return Total Return on to-Market on Cash P&Lto Variation Total P&L Date Yield Value Cash flow Flow Date Value Margin to Date 1 2.0 8,927,737 −8,927,740 0 0 0 0 0 2 2.1 8,001,468 −496 −926,765 −926,765 0 −926,765 3 2.1 8,001,935 −521 −926,819 −926,765 −54 −926,819
Table 5 shows that the total profit and loss to date of an off-market, uncleared swap can be replicated by a non-biased, centrally-cleared swap future created pursuant to the principles of the present invention each day.

EXAMPLE 6

[0077] An embodiment of a non-biased, centrally-cleared financial instrument in accordance with the principles of the present invention can trade as an interest-rate swap future and defines its terminal value according to the foregoing definition with a constant of 100 added to the futures price to be consistent with market convention. In this example, this embodiment will be referred to as the “total-return swap future”. The initial price of a swap future with a par coupon is 100.

[0078] In this example, the total-return swap future is compared with an interest-rate swap cleared through IDCG. Two points are highlighted through this comparison. First, as a main feature of the IDCG interest-rate swap, fixed and floating coupon payments, as defined by the terms of the swap, are exchanged bilaterally when they become due. The total-return swap future replicates the economic effect of the coupon payments without requiring bilateral payments by having the definition of terminal value include the net accumulation of cash flows. Second, since the IDCG swap generates daily variation margin, without appropriate adjustment, the total profit and loss on the IDCG swap is not equivalent to an uncleared swap as a result of both the convexity bias and the NPV effect.

[0079] Assume two different 10-year spot starting par swaps with a notional value of $100 M as in Example 1 are traded as a total-return swap future and on IDCG simultaneously. Both are centrally cleared. The par coupon of the total-return swap future is 2.0%, equal to the prevailing yield. For the purpose of comparison, assume the IDCG cleared swap is traded at the same coupon.

[0080] To show that the total-return swap future replicates the economic effect of the coupon payments without requiring bilateral payments, Table 6a compares the cash flow and the profit and loss of the total-return swap future with the IDCG cleared swap before and after a payment is due pursuant to the terms of the swap. Assuming the yield does not change from day 1 to day 90, a floating payment of $500,000 is payable from the buyer to the seller.

TABLE-US-00006 TABLE 6a Comparison of IDCG Cleared Swap and Total-Return Swap Future IDCG Cleared Swap Coupon = 2 Accum. Total-Return Swap Future Marked Interest Coupon = 2 to Accum. on Total Settle- Return on Total Market Coupon Variation Coupon P&L to ment Variation P&L to Date Yield Value Payment Margin Payment Date Price Margin Date 90 2.0 500,000 −500,000 0 0 0 100 0 0 91 2.0 500,028 28 −28 0 100 0 0
Table 6a shows that the total profit and loss to date of a total-return swap future is the same as that of an IDCG cleared swap without requiring bilateral coupon payments.

[0081] To demonstrate that the IDCG cleared swap without appropriate adjustment is not equivalent to an uncleared swap, assume the yield changes to 2.1% on day 92. Table 6b compares the cash flows and profit and loss of the IDCG cleared swap and the total return swap future:

TABLE-US-00007 TABLE 6b Comparison of 1 DCG Cleared Swap and Total Return Swap Future after Yield Change DDCG Cleared Swap Coupon = 2 Total-Return Swap Future Accum. Coupon = 2 Interest Return Marked to Accum. on Total Settle- on Total Market Coupon Variation Coupon P&L to ment Variation P&L to Date Yield Value Payment Margin Payment Date Price Margin Date 92 2.1 −417,744 −917,744 −57 −917,800 99.0822 0 −917,800 93 2.1 −417,768 −917,822 −86 −917,908 99.0822 −54 −917,854
Table 6b shows that the total profit and loss to date on the IDCG cleared swap is different from that of the total return swap future. As already seen from previous examples, the non-biased, centrally-cleared swap future created in accordance to the principles of the present invention is economically equivalent to an uncleared swap. Therefore the IDCG cleared swap, without proper adjustments, does not generate the same profit and loss as an uncleared swap. The reason for this discrepancy in the total profit and loss to date is because all of the changes in net present value of the IDCG swap flow to and from the buyer through variation margin, causing the NPV effect to be present. And further, because the accumulated variation margin accrues interest at a rate that is correlated with the marked-to-market value of the IDCG swap, the convexity bias is also partly responsible for the discrepancy in the profit and loss.

EXAMPLE 7

[0082] The following example illustrates the NPV effect in the case of a cleared credit default swap (CDS) without adjustment. Consider two counterparties enter into a $10 M notional value, 5-year CDS with XYZ Corp as the reference entity, at a premium of 500 basis points of the notional amount per annum (known as the spread). This obligates the buyer to pay $125,000 ($10 M*5.0%/4) to the seller every quarter for 5 years, or until the default of XYZ Corp if the default occurs before the maturity of the CDS. In return, the buyer will receive $10 M if XYZ Corp defaults within the 5-year period of the CDS. To simplify this example, the default risk of XYZ Corp is assumed to be uncorrelated with interest rates; that being the case, a cleared CDS would have traded at the same spread (i.e. 500 basis points) in the absence of convexity bias. Assume that immediately after the trade is consummated, the market assessment of the default risk of XYZ Corp changes, and the spread of a 5-year XYZ Corp CDS is now 300 basis points. The following will compare the profit and loss between an uncleared CDS, a cleared CDS without adjustment for the NPV effect, and a non-biased, centrally-cleared financial instrument created in accordance with the principles of the current invention.

[0083] In the case of an uncleared CDS, the marked-to-market value of the original CDS with 500 basis point spread is equal to the sum of the present value of a stream of −$50,000 ($10 M*(−5.0%+3.0%)/4) quarterly payments until the maturity of the CDS or the default of XYZ Corp, whichever comes first, or approximately −$758,432 assuming an interest rate of 6.0% and a certain probability of default. If the buyer unwinds the position at that time, a loss of −$758,432 is realized.

[0084] Consider a cleared CDS without adjustment where the exchange or the clearinghouse requires the daily settlement to be equal to the net present value of an uncleared CDS. Since the net present value of the CDS at the end of day one is −$758,432, a loss of the same amount occurs to the buyer through the variation margin. However, even after the variation margin flows, the buyer needs to pay a certain amount to unwind the position. To see this, consider a third party “buys” this CDS from the original buyer with no payment. The credit risk can be hedged by selling a new CDS at the spread of 300 basis points with the same notional value and maturity. The net marked-to-market value of long a CDS at 500 basis points and short a CDS at 300 basis points will decrease from −$758,432 to −$1,000,000 (−$50,000*4*10), if the default does not occur before the maturity, and otherwise to a value between -$758,432 and −$1,000,000. The present value of this stream of negative cash flow is approximately −$153,334, which is the fair price that the original buyer has to pay to the third party to unwind its position. The total loss from trading this cleared CDS is thus significantly more than that from trading the uncleared CDS. This is caused by the NPV effect.

[0085] Now consider the non-biased, centrally-cleared financial instrument created in accordance with the principles of the present invention. On day one, after the CDS spread changes to 300 basis points, the fair settlement value will be equal to the net present value of the uncleared CDS, i.e., −$758,432. The buyer can unwind its position by entering a short position in a new CDS with the spread of 300 basis points and the same notional value and maturity. The terminal value of these long and short positions, in accordance with the present invention, is equal to the accumulated value of a stream of −$50,000 paid quarterly until the maturity of the CDS or the default of XYZ Corp, whichever comes first, minus the accumulated value of all the interest paid for this stream of negative cash flows. Therefore, the terminal value is equal to the present value of this stream of negative cash flows, or −$758,432. The buyer will have no additional profit or loss, and the loss of $758,432 is locked in on day one. Thus, the centrally-cleared financial instrument has the same economic effect as the uncleared CDS when the CDS spread changes.

[0086] This concludes the Examples of non-biased, centrally-cleared financial instruments created by adjusting the terminal value for the interest on variation margin in accordance with the principles of the present invention.

[0087] A non-biased, centrally-cleared financial instrument in accordance with the principles of the present invention may be transacted by a variety of means, including but are not limited to a trading floor, telephone or electronically. After the trade has been agreed to by the buyer and seller, whether it is in a private communication or a publicly accessible medium, a financial instrument of the present invention will then be submitted to a clearinghouse for central clearing. A further aspect of the present invention relates to the electronic clearing and settling of such non-biased, centrally-cleared financial instruments.

[0088] In accordance with the principles of the present invention, on a periodic, generally daily basis, the exchange or clearinghouse may determine and publish a settlement price for a non-biased, centrally-cleared financial instrument. The settlement price of the non-biased, centrally-cleared financial instrument is determined by the market price at which the non-biased, centrally-cleared financial instrument is quoted or traded on each day. In the case where a market price is not directly observed, the non-biased, centrally-cleared financial instrument should be settled at a value that is consistent with other related financial instruments whose market prices are observable. In such case, the financial instrument can be settled at a value equal to a sum of present value of remaining asset flows, plus accumulated value of past asset flows, minus accumulated return on variation margin.

[0089] Take a non-biased, centrally-cleared, interest-rate swap as an example; if a non-biased, centrally-cleared swap created according to the present invention does not have a market price on a particular day, the exchange or clearinghouse will settle the interest-rate swap to a value equal to the sum of the present value of remaining cash flows, plus the accumulated value of past cash flows, minus the accumulated total return on variation margin to date. The evaluation of cash flows utilizes a yield curve constructed using other liquid, interest-rate swaps or interest-rate financial instruments; therefore, consistency with the value of a liquid, non-biased, centrally-cleared, interest-rate swap is guaranteed.

[0090] The following is a non-limiting example of a daily settlement methodology implemented for a centrally-cleared interest-rate swap in accordance with the principles of the current invention.

EXAMPLE 8

[0091] Consider the 10-year interest-rate swap set forth in Example 1. On the day the trade is consummated, the non-biased, centrally-cleared swap is settled to its present value according to the following standard practice of valuing interest-rate swaps: First, a yield curve is built from the current cash deposit rates, LIBOR, Eurodollar futures, and swap rates for a list of key maturities: 3 year, 4 year, 5 year, 10 year, 15 year, 20 year, and 30 year. Using a “bootstrapping” method, the yield curve is constructed from those rates or instruments.

[0092] Second, the present value of the fixed leg is computed as:

[00005]$P{V}_{\mathrm{fixed}}=C\times P\times \underset{i=1}{\overset{M}{.Math.}}\left(\frac{t_i}{T_i}\times {\mathrm{df}}_i\right),$

where P is the notional amount, C is the fixed coupon of the swap, M is the number of the fixed payments, t.sub.i is the number of days in period i, T.sub.i is the basis according to the day count convention, and df.sub.i is the discount factor derived from the yield curve constructed as above for the i.sup.th fixed coupon payment. Third, the present value of the floating leg is computed as:

[00006]$P{V}_{\mathrm{fixed}}=P\times \underset{j=1}{\overset{N}{.Math.}}\left(f_j\times \frac{t_j}{T_j}\times {\mathrm{df}}_j\right),$

where N is the number of the floating payments and f.sub.j is the forward rate for the time period j. Finally, the present value of the swap is computed as PV.sub.fixed−PV.sub.float .

[0093] A non-biased, centrally-cleared, interest-rate swap with the par coupon of 2.0% as in Example 1 is settled at 0 on day 1.

[0094] On day 2, assume the yield curve shifts upwards by 10 basis points. The settlement value of this non-biased, centrally-cleared interest-rate swap is computed as the present value of remaining cash flows of the swap, plus the accumulated value of past cash flows, minus the accumulated total return on variation margin to date. The present value of remaining cash flows is equal to PV.sub.fixed−PV.sub.float=$9,093,503−$10,000,000=−$906,497. The accumulated value of past cash flow is 0 as no coupon payment has been made, and the accumulated total return on variation margin is 0 since no variation margin has been generated since the initial trading day. Therefore the settlement value of the non-biased, centrally-cleared interest rate swap is equal to −$906,497 on day 2.

[0095] On day 3, assume there has been no change in the yield curve since day 2. The present value of remaining cash flows is equal to PV.sub.fixed−PV.sub.float=$9,093,450 −$10,000,000=−$906,550. The accumulated value of past cash flows is still 0. The accumulated total return on variation margin, currently −$906,497, is equal to the −$53 (−$906,497*2.1%365). Therefore, the settlement value on day 3 is equal to $−906,497(−$906,550−(−$53)).

[0096] The non-biased, centrally-cleared financial instrument may be marked to market, generally daily, using its settlement price. On the same time scale that a settlement value is published, generally daily, the clearinghouse can compute the variation margin requirement for each non-biased, centrally-cleared financial instrument. Cash flow payments reflecting the variation margins will flow between the clearinghouse and parties holding open positions in non-biased, centrally-cleared financial instruments on a periodic, generally daily basis.

[0097] The clearinghouse must store and maintain the historical data series of daily settlement values for each financial instrument, as well as the overnight interest rate. These, in addition to the initial trade price, are required for determining the terminal value and may be stored in a database and can be published to the marketplace.

[0098] On the last day of the existence of the non-biased, centrally-cleared financial instrument, generally known as expiration, the clearing house will compute and settle the non-biased, centrally-cleared financial instrument to the terminal value as defined according to the principles of the present invention. As previously described, in one example a non-biased, centrally-cleared financial instrument of the present invention can be cleared and settled utilizing a terminal value determined in accordance with the previously detailed alternative embodiments.

[0099] According to the principles of this invention, in order to publish daily and terminal settlement values, a clearinghouse, exchange, futures commission merchant or other market participant may use computers with software specifically designed for this purpose. The computation of the terminal value in accordance with the present invention is iterative and complex, and special software is required for this purpose. This software may be linked to a centralized marketplace via data lines, networks or the Internet, so that the prices are published in a seamless manner. The clearing house may store the daily prices for each financial instrument in existence at any given moment in a database and can be electronically published to the marketplace.

[0100] Referring to FIG. 3, a non-limiting example of a high level hardware implementation can used to run a system of the present invention is seen. The infrastructure should include but not be limited to: wide area network connectivity, local area network connectivity, appropriate network switches and routers, electrical power (backup power), storage area network hardware, server-class computing hardware, and an operating system such as for example Redhat Linux Enterprise AS Operating System available from Red Hat, Inc, 1801 Varsity Drive, Raleigh, N.C.

[0101] The clearing and settling and administrative applications software server can run for example on an HP ProLiant DL 360 G6 server with multiple Intel Xeon 5600 series processors with a processor base frequency of 3.33 GHz, up to 192 GB of RAM, 2 PCIE expansion slots, 1 GB or 10 GB network controllers, hot plug SFF SATA drives, and redundant power supplies, available from Hewlett-Packard, Inc, located at 3000 Hanover Street, Palo Alto, Calif. The database server can be run for example on a HP ProLiant DL 380 G6 server with multiple Intel Xeon 5600 series processors with a processor base frequency of 3.33 GHZ, up to 192 GB of RAM, 6 PCIE expansion slots, 16 SFF SATA drive bays, an integrated P410i integrated storage controller, and redundant power supply, available from Hewlett-Packard.

[0102] While the invention has been described with specific embodiments, other alternatives, modifications, and variations will be apparent to those skilled in the art. Accordingly, it will be intended to include all such alternatives, modifications and variations set forth within the spirit and scope of the appended claims.