Introduction to Eris Exchange Interest Rate Swap Futures

Transcription

1 Introduction to Eris Exchange Interest Rate Swap Futures Overview Eris Exchange interest rate swap futures ( Eris contracts ) have been designed to replicate the net cash flows associated with plain-vanilla, fully collateralized OTC interest rate swaps, as encompassed in the Eris Methodology TM, while retaining all of the operational and economic efficiencies of traditional futures contracts. This paper examines the features and pricing formulas applied to the Eris contract. Settlement Price Calculations Eris interest rate swap futures are priced on a basis of 100, similar to market practice for bonds and other futures contracts. This discussion can be applied to both spot and forward starting contracts which are described in the following document located on the Eris Exchange web site: Eris Interest Rate Swap Futures - Detailed Contract Specifications The settlement value for the Eris contract is defined as: Where S t is the settlement price at time t, A t is the net present value ( NPV ) of the future fixed and floating amounts at time t, B t is the value of the historical fixed and floating amounts since contract inception, and C t is the Eris Price Alignment Interest (or Eris PAI TM ). 100 is a constant that acts as an index price. The purpose of the 100 index price is to reduce the likelihood that the Eris contract price becomes a negative number as rates fluctuate. Negative prices can present challenges for traditional clearing systems. A t is the net present value of all future fixed and floating amounts. For settling Eris contracts, the OIS curve is used to construct the LIBOR forward curve and to discount fixed and floating cash flows to present value. The curve is supplied by CME Clearing and is the same as is used by CME Clearing to settle cleared OTC interest rate swaps. ( ) ( ) [2] L i is the floating coupon at time t i, F i is the fixed coupon at time t i and D(t,t i ) is the value at time t of a riskless zero coupon bond worth 1 at t i. A t may include interest from the prior fixed and floating swap reset dates that apply to the current period. [1] 1

2 B t, the value of the historical fixed and floating amounts since contract inception: [3] Where t i is the initial time, t is the current time, CF i is the net of the fixed and floating amounts that would be paid/received at t i, if this was an OTC interest rate swap. It is important to understand the distinction between treatment of collateral in un-cleared OTC IRS and variation margin in futures. Un-cleared OTC IRS Collateral: When a trade moves against a party they are required to post collateral to the other party. The party posting collateral retains legal ownership of that collateral and will be paid interest by the party holding that collateral (i.e., the inthe-money party). The collateral transfer terms and interest rate paid on collateral are defined in the Credit Support Annex ( CSA ) to the ISDA Master Agreement between the two parties to the trade. We assume that the CSA has a $0 threshold and the interest rate is the overnight Fed Funds rate. Futures Variation Margin: When a futures contract moves against a party, there is a requirement to post variation margin to the clearinghouse. The clearinghouse will then credit the margin account of the other party in the trade (i.e., the in-the-money party). The party receiving the margin is the legal owner of those funds. Because the party posting margin is no longer the owner of the collateral, they do not receive interest on the funds that they have posted. C t is an adjustment to the value of the Eris contract to compensate the party posting margin for interest that would have been earned in an analogous un-cleared OTC IRS. This is also referred to as Eris PAI TM. The traditional concept of PAI for interest rate swaps involves discrete daily interest payments between the counterparties to a contract. This is the approach employed by other market entities including some centralized counterparties. In order to track the total value of the swap throughout the life of its existence, the Eris contract embeds the cumulative PAI throughout the life of the contract into the daily settlement price. This accumulation of daily interest adjustments allows the contract to be traded on equivalent economic terms, without up-front payments, by any Eris Exchange market participant. It is not relevant which parties bought and sold the original contract. ( ) [4] 2

3 Substituting [1]: ( ) [5] Taking the terms above, and looking at the daily returns on an Eris contract, from equation [1]: Substituting [4] and [5], [6] can be rewritten as: ( ) [6] ( ) ( ) [7] Interpreting this, ( ) is the change in the value of an un-cleared OTC IRS. Any changes in NPV due to fixed and floating amounts are balanced by the corresponding change in the value of B; ( ). The first two terms of the daily change in value are identical to those of an un-cleared OTC IRS. The final term, replicates what would have been interest on the previous day s collateral if this had been a bilateral OTC swap with a CSA having a $0 threshold. 3

4 Examples Below are step-by-step examples showing the valuation and settlement procedure for an Eris contract over the course of several days, and at different points during the life of the contract. Example 1: Initiating a Trade Trader #1 buys 1 Eris contract from Trader #2: Buy means to pay fixed or to have a long position 1 contract represents $100,000 notional 2 year contract at a 2% fixed rate Trade executed on 12/1/200 Tables 1 and 2 illustrate cash flow dates, and accrual periods: Table 1 Reset Dates Accrual Start Fixed Accrual End Day Count Year Fraction 6/3/ /3/200 6/3/ /3/2009 6/3/ /3/ /3/ /3/2009 6/3/ /3/2010 6/3/ /3/ Table 1 was generated to illustrate semi-annual fixed rate cash flows using a 30/360 day count. Each LIBOR settling is determined 2 business days prior to the fixing period. Quarterly amounts are generated using an Actual/360 day-count. Table 2 ing Fixing Date Reset Date Accrual Start Accrual End Day Count Year Fraction 12/1/200 3/3/ /3/200 3/3/ /27/2009 6/3/2009 3/3/2009 6/3/ /1/2009 9/3/2009 6/3/2009 9/3/ /1/ /3/2009 9/3/ /3/ /1/2009 3/3/ /3/2009 3/3/ /1/2010 6/3/2010 3/3/2010 6/3/ /1/2010 9/3/2010 6/3/2010 9/3/ /1/ /3/2010 9/3/ /3/

5 At the time of the trade initiation, the LIBOR rate would be ~1.9701%, for the Eris contract to have an initial value of 0. For purposes of the example, we assume that the OIS curve is flat at 1% for all tenors. Present Value totals for Fixed and ing legs are calculated using the unrounded present value amounts determined when multiplying the Amount by the Discount Factor. OIS discount factors below are generated using an Actual/360 day-count, where the Actual days are calculated from t+0. Table 3 Fixed Reset Date Year Fraction Amount Discount Factor Present Value 6/3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ Total: $3, Table 4 Reset Date ing Year Fraction Amount Discount Factor Present Value 3/3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $47.97 Total: $3, We now assume that at the end of the day the swap was executed, the LIBOR forward curve is flat at 2%. We can determine the NPV of the transaction. 5

6 Table 5 Fixed Reset Date Year Fraction Amount Discount Factor Present Value 6/3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ Total: $3, Table 6 ing Reset Date Year Fraction Amount Discount Factor Present Value 3/3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ Total: $4, The current methodology is for individual components of the Eris futures price to be calculated to decimal places, and for the Eris Futures price to be rounded to 4 decimal places. For purposes of these examples, we will ignore those constraints. Per Contract NPV 0 = NPV floating NPV fixed = $4, $3, = $ The values of the various components can be to express the contract value on a 100 basis A 0 = / = As no fixed or floating dates have been crossed, B = $0 Because there has been no margin held overnight, Eris PAI TM = $0 Settlement Price for this swap on the first day would be: S 0 = A 0 + B 0 - C 0 6

7 S 0 = = Moving forward to the next day, if the LIBOR swap and OIS curves are unchanged overnight, then the only change in the NPV of the swap comes from the slight change in discount factors as the cash flow days are now one day closer. Table 7 Fixed Reset Date Year Fraction Amount Discount Factor Present Value 6/3/ $ $ /3/ $ $99. 6/3/ $ $ /3/ $ $ Total: $3, Table ing Reset Date Year Fraction Amount Discount Factor Present Value 3/3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ /3/ $ $ Total: $4, Per Contract NPV 1 = $4, $3, = $ NPV 1 = / = = A 1 B 1 = 0 Eris PAI TM 1 = (S B 0 + Eris PAI TM 0)r 0 Δt 0 + Eris PAI TM 0 = C 1 Eris PAI TM 1 = ( )*1%*(1/360) + 0 = = C 1 S 1 = A 1 + B 1 - C 1 S 1 = =

8 Example 2: Period covering a fixed and floating reset date Consider the same contract used in Example 1. On 3/2/2009, one day before the first floating amount occurs, assume the initial values are as follows: Per Contract NPV 3/2/2009 = $2, A 3/2/2009 = 2,500 / = 2.5 B 3/2/2009 = 0 Per Contract C 3/2/2009 = $5 C 3/2/2009 = 5 / = S 3/2/2009 = = = A 3/2/ B 3/2/ C 3/2/2009 On 3/3/2009, at settlement, the amount shifts from the A to the B. In a traditional OTC IRS, this would be a cash payment. Per Contract NPV 3/3/2009 = $2, NPV 3/3/2009 = 2, / = 2.0 = A 3/3/2009 Per Contract B 3/3/2009 = $ B 3/3/2009 = / = 0.5 C 3/3/2009 = A 3/2/2009 r 3/2/2009 Δt 3/2/ C 3/2/2009 = C 3/3/2009 C 3/3/2009 = $2,500*1%*1/360 + $5 = $ = C 3/3/2009 S 3/3/2009 = = = A 3/3/ B 3/3/ C 3/3/2009 Performing the same calculations for 3/4/2009, Per Contract NPV 3/4/2009 = $2, NPV 3/4/2009 = 2, / = 2.0 = A 3/4/2009 B 3/4/2009 = $500 Per Contract C 3/4/2009 = $2,000*1%*1/360 + $ = $5.12 C 3/4/2009 = 5.12 / = S 3/4/2009 = = = A 3/4/ B 3/4/ C 3/4/2009

9 Example 3: Swap is unwound Assume that during the trading day on 3/4/2009 Trader #1 wants to unwind the position. Recall from Example 2 that B 3/4/2009 and C 3/4/2009 have already been established and will remain static throughout the day: B 3/4/2009 = 0.5 C 3/4/2009 = Trader #1 will solicit unwind values from market participants which will be expressed in price (USD) as is the market practice for unwinds of OTC IRS. The unwind quotes represent A, which is the NPV per contract: Trader #3 Unwind NPV: $2,100 Trader #4 Unwind NPV: $1,950 Trader #5 Unwind NPV: $1,90 Trader #1 will choose the highest unwind NPV of $2,100 from Trader #3 and execute the unwind transaction. This equates to 2.1 on a 100 basis (2,100 / ). Unwind Price = A unwind + B 3/4/2009 C 3/4/2009 Unwind Price = = Because the unwinding party executed the contract at 100, the total value realized is: Trader #1 P&L = ( ) * = $2,595 Trader #1 will monetize the P&L through funds in the margin account. In this case, the margin account will need to be adjusted by the clearinghouse following the unwind. The current balance in the margin account is the difference between the prior settlement and the purchase price of the contract, which is less than the unwind amount less the purchase price: Margin account value: ( ) * = $2,495 Because the Unwind Price is $100 higher than the prior settlement value, S 3/4/2009, the clearinghouse will pay trader #1 $100 in variation margin on 3/4/2009: Unwind Price - S 3/4/2009 = = 0.10 Amount due to Trader #1 by clearinghouse = 0.10 * = $100 The party that transacts the unwind, Trader #3, will replace Trader #1 as the holder of the contract. 9

10 At the end of the trading day on which the unwind occurred, the position will be revalued and required variation margin will be determined. For example: If the Eris futures price is , Trader #3 s margin account will be increased by $405. This value represents the difference between the end of day value and the Unwind Price: $405 = ( ) * If the Eris contract value is , Trader #3 s margin account will be reduced by $595. This value represents the difference between the end of day value and the Unwind Price: -$595 = ( ) * If the Eris contract value at the end of the day is equal to Unwind Price, the new party s margin account will not change Trader #2, the original Eris contract seller, will continue to post and/or receive variation margin as in prior periods. o Trader #2 will not know that Trader #1 has unwound their position unless they were a bidder in the unwind process 10

11 Eris Exchange Publicly Available Files Eris Exchange strives for transparency in how we value our instruments. This ensures that Interest Rate Swap Futures can be traded anonymously and fairly within the marketplace. To that end, we publicly disseminate output files that describe how Eris Exchange interest rate swap futures are valued. A list of those files, and descriptions of the data in those files, can be found below. Name Description File Name Delivery Time 1. Eris Exchange BOD Pricing File #1 Published after the close of each trading day and includes B & C values that will be used to calculate the Eris futures price for the new trading date. At :30am ET on the following business day, all Eris contracts will trade with a futures price using the C component that is published in the BOD Pricing File #2. Eris_Instruments_YYYYMMDD_Prices_Prev_PAI_Rate.csv 5:35 pm ET (4:35 pm CT) 2. Eris Exchange BOD Pricing File #2 Eris Exchange beginning of day pricing file provides a list of all tickers, previous day s settlement prices, and B & C values calculated using the Fed Funds Rate published by the New York Federal Reserve that morning. 2 Eris_Instruments_YYYYMMDD_Prices_TopDay_PAI_Rate.csv :25 am ET (7:25 am CT) 3. Eris Exchange EOD Pricing File End of day pricing file that incorporates the A (NPV) + B (Historical fixed and floating amounts) - C ( Eris PAI TM ) calculation to derive the daily settlement price for open tickers. Eris_Instruments_YYYYMMDD_EOD_Settles.csv 4:45 pm ET (3:45 pm CT) 2 In the event that the current day s Fed Funds Effective rate is not available by :26am ET for a given trading day, Eris Exchange s policy is to use the most recent historical rate to calculate the BOD Pricing File. However, Eris Exchange reserves the right to exercise discretion in delaying daily processes until after the top day rate is published. 11

12 4. Eris Exchange Curve File The Eris Curve as of 3:00 pm NY time, incorporating LIBOR cash flow amounts with OIS discounting. Column A shows the duration (2y to 30y), and Column L (labeled FairCoupon (%) ) shows the coupon rate that would result in a zero- NPV swap. Eris_YYYYMMDD_EOD_ParCouponCurve_OIS.csv 4:45 pm ET (3:45 pm CT) 5. Eris Exchange LIBOR Discount Factor File Daily LIBOR discount factors, spot rates and 3-month fixings for 30 years. Eris_YYYYMMDD_EOD_DiscountFactors_LIBOR.csv 4:45 pm ET (3:45 pm CT) 6. Eris Exchange OIS Discount Factor File Daily OIS discount factors and spot rates for 30 years. Eris_YYYYMMDD_EOD_DiscountFactors_OIS.csv 4:45 pm ET (3:45 pm CT) 7. Eris Exchange Swap Leg Price File Daily pricing file that shows the fixed and floating payment dates and rates for Eris Exchange tickers, including most recent reset rate for floating leg. Eris_YYYYMMDD_EOD_PricedSwapLegAnalysis_OIS.csv 4:45 pm ET (3:45 pm CT). Eris Exchange Swap Holidays File Daily files that shows the every exchange holiday for the next 40 years. Eris_YYYYMMDD_EOD_Holidays.csv 4:45 pm ET (3:45 pm CT) 12

13 Eris Exchange EOD Pricing File Column Heading Description of Data Data Format Units Decimal Places Symbol The exchange assigned symbol, based on Tenor Bucket and a counter to differentiate between similar instruments. For more information on how tickers are created, please see Ticker Symbology. Example: ZA0001 String NA NA Final Settlement Price This is the settlement price published by CME. 4 Evaluation Date This is the date the file was processed. Date MM/DD/YYYY NA First Trade Date This represents the date the trade was initiated. Date MM/DD/YYYY NA Eris PAI Date Effective Date CashFlow Alignment Date The date from which return on variation margin will start to accrue. Eris PAI TM will be non-zero on the first business day after this date. The start date of the first accrual period. For Spot Starting Swaps, this is 2 days after the First Trade Date, subject to NY and London holiday calendars. The date selected at the time of the trade for setting up cash flow (payment) dates for Eris contracts. Date MM/DD/YYYY NA Date MM/DD/YYYY NA Date MM/DD/YYYY NA 13

14 Maturity Date The final day of the contract. Cash Flow Alignment Date adjusted by Modified Following on the Joint NY/London Calendar Date MM/DD/YYYY NA NPV (A) This value corresponds to NPV t in the equations used in this paper. The NPV represents net present value of the future cash flows at time t. This is also one of the primary inputs needed for calculating a futures price for an interest rate swap future, using the calculation of Futures Price = 100+A+B-C. NPV is per 100 notional. Fixed NPV The NPV (Net Present Value) for the fixed leg of the trade, calculated that day. NPV is per 100 notional. ing NPV The NPV (Net Present Value) for the floating leg of the trade, calculated that day. NPV is per 100 notional. Coupon (%) The agreed upon fixed rate for the interest rate swap future. Rate in % 6 Fair Coupon (%) The coupon that would have resulted in NPV = 0. Rate in % Fixed Payment Fixed Payment that occurs on the Evaluation Date. Payment is for 100 Notional. 14

15 ing Payment ing Payment that occurs on the Evaluation Date. Payment is for 100 Notional. Next Fixed Payment Date The date the next fixed payment will be made. Date MM/DD/YYYY NA Next Fixed Payment Amount The next fixed payment amount. Previous Fixing Date The date the floating rate was set for the next floating payment Date MM/DD/YYYY NA Previous Fixing Rate The 3 month LIBOR rate applied to the ing leg for that instrument. Rate in % Next ing Payment Date The date the next floating payment will be made Date MM/DD/YYYY NA Next ing Payment Amount The next floating payment amount. Next Fixing Date The date at which the 3 month LIBOR rate will be assigned for the next floating leg period. Date MM/DD/YYYY NA Previous Settlement Date This value corresponds to t-1 in the equations used in this paper. Date MM/DD/YYYY NA 15

16 The last business day a settlement price was calculated. Previous Settlement Price This value corresponds to S t-1 in the equations used in this paper. Settlement price calculated on Previous Settlement Date. Previous Eris PAI This value corresponds to Eris PAI TM t-1 in the equations used in this paper. The Eris PAI TM on the Previous Settlement Date. Fed Funds Date Fed Funds Rate (%) Accrual days The date that the for which the fed funds date was published (for example, a date of 4/12/2011 means that the rate was published on 4/13/11 by the NY Federal Reserve and applies from 4/12/2011 to 4/13/2011). Rate accrues from this date forward one business day. This value corresponds to r t-1 in the equations used in this paper. The Fed Funds Rate published for the Fed Funds Date by the New York Federal reserve Bank. Rate is published at approximately 7AM CST for accruals overnight from previous business day to today. How many days have passed since settlement price was last calculated. This value is generally 1, but accounting for weekends and holidays, could be greater than 1. Date MM/DD/YYYY NA Rate in % Int Days 0 Daily Incremental Eris PAI This number represents the day over day variation margin for 1 contract for this instrument ID, or Eris PAI TM t Eris PAI TM t-1. As this instrument is a future and not a swap, margin is posted using variation margin as opposed to collateral. Whereas the holder of collateral retains any interest made off that collateral, 16

17 interest is returned to the customer for variation margin. In order to mimic the economics of OTC swaps, interest on variation margin is included in the overall futures price of the instrument. Accrued Coupons (B) This value corresponds to B t in the equations used in this paper. As this instrument is a future and not a swap, no payments actually change hands throughout the life of the contract. This value represents accumulated fixed and floating amounts, and is one of the primary inputs needed for calculating a futures price for an interest rate swap future, using the calculation of Futures Price = 100+A+B-C. Eris PAI (C ) This value corresponds to Eris PAI TM t in the equations used in this paper. Eris PAI TM is the cumulative daily interest adjustment. As this instrument is a future and not a swap, margin is posted using variation margin as opposed to collateral. Whereas the holder of collateral retains any interest made off that collateral, interest is returned to the customer for variation margin. Eris PAI TM is one of the primary inputs needed for calculating a futures price for an interest rate swap future, using the calculation of Futures Price = 100+A+B-C. Settlement Price (100+A+B-C) The settlement price for the instrument, calculated that day. 17

18 RFQ NPV Tick Size The minimum NPV increment, in dollars, that can be used to price Requests for Quotes. This is based on the tenor of the interest rate swap futures. Int contract $1 for Contracts where the lesser of Remaining Tenor/Underlying Tenor is less than two years. $2 for Contracts where the lesser of Remaining Tenor/Underlying Tenor is greater than or qual to 2 years and less than 4 years. $5 for Contracts where the lesser of Remaining Tenor/Underlying Tenor is greater than or equal to 4 years and less than 7 years. $10 for Contracts where the lesser of Remaining Tenor/Underlying Tenor is greater than or equal to 7 years and less than 20 years. $20 for Contracts where the lesser of Remaining tenor/underlying Tenor is greater than or equal to 20 years Nominal This is the notional value used to calculate NPV s and Fixed and ing Payment amounts. A notional of 100 is used to calculate the settlement price because the point value of the futures contract is $. Eris contract notional is $100,000. Int Base value for an Eris Contract 0 Product Code The first 6 characters in the instrument ID. This shows Tenor Bucket and a counter to differentiate between similar instruments. String NA 0 Tenor Category Denotes the initial tenor for the instrument. String Self-defining 0 1

19 Eris Exchange, LLC Legal Notice 06/02/15 Futures trading is not suitable for all investors, and involves the risk of loss. Futures are a leveraged investment, and because only a percentage of a contract s value is required to trade, it is possible to lose more than the amount of money deposited for a futures position. Therefore, traders should only use funds that they can afford to lose without affecting their lifestyles. And only a portion of those funds should be devoted to any one trade because they cannot expect to profit on every trade. All references to options refer to options on futures. Trading on Eris Exchange is limited to those persons who are eligible contract participants as defined in 1a (12) of the Commodity Exchange Act. Notice to individuals located in the United Kingdom. The materials contained in this communication are directed only at persons with investment experience (i.e., investment professionals ). Persons who do not have professional experience in matters relating to investments should not rely on any of the information herein. The investment activities to which these materials relate are only available to persons with investment experience. Any request to engage in the investment activities to which these materials relate, by persons other than those with investment experience, shall be denied. Eris Exchange and the Eris Logo are registered trademarks of Eris Exchange, LLC. Eris SwapBook, Eris BlockBox, and Eris PAI are trademarks of Eris Exchange, LLC. The information within this document has been compiled by Eris Exchange for general purposes only. Eris Exchange assumes no responsibility for any errors or omissions. Additionally, all examples in this document are hypothetical situations, used for explanation purposes only, and should not be considered investment advice, legal advice, or the results of actual market experience. The information contained within this document does not constitute legal or investment advice. All matters pertaining to rules and specifications herein are made subject to and are superseded by official Eris Exchange rules. Current rules should be consulted in all cases concerning contract specifications. Copyright 2015 Eris Exchange LLC. All rights reserved. 19