A Guide to the Pricing Conventions of SFE Interest Rate Products


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1 A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios SFE 90 Day Bak Bill Optios Australia Commowealth Treasury Bods SFE 10 Year Treasury Bod Futures SFE 10 Year Treasury Bod Futures Tick Value Calculatios SFE 10 Year Treasury Bod Optios SFE 3 Year Treasury Bod Futures Tick Value Calculatios SFE 3 Year Bod Optios Iterest Rate Swap Futures 3 Year Iterest Rate Swap Futures 10 Year Iterest Rate Swap Futures This brochure provides market users ad back office system suppliers with a guide as to the pricig covetios of SFE iterest rate futures ad optios. The pricig covetios used for the majority of SFE's iterest rate products differ from that used i may offshore futures markets. Ulike i Europe ad the Uited States where iterest rate securities are traded i the cash market o the basis of their capital price, the covetio adopted i Australia is to price such istrumets o the basis of their yield to maturity. Due to this covetio, SFE's iterest rate cotracts are similarly traded o the basis of yield with the futures price quoted as 100 mius the yield to maturity expressed i per cet per aum. While the obvious advatage of pricig iterest rate cotracts i this fashio is that their yield is trasparet ad ca be easily compared to yields o cash market istrumets, a importat byproduct is that the tick value o these products does ot remai costat but rather chages i accordace with movemets i the uderlyig iterest rate. This variatio is most proouced i the 10 Year Treasury Bod futures cotract ad is less substatial for the 3 Year Treasury Bod futures cotract ad 90 Day Bak Bill futures cotracts. For all these cotracts, the tick value decreases as iterest rates rise ad icreases as iterest rates fall. 30 Day Iterbak Cash Rate Futures Ulike SFE s 90 day Bak Bill Futures ad 3 ad 10 year Treasury Bod Futures, the 30 Day Cash Rate Futures cotract has a fixed tick. Uder a fixed tick regime, the variatio margis are calculated by multiplyig the umber of price movemets (i poits terms) by the fixed tick dollar value of AUD24.66 per 0.01% move by the umber of cotracts traded. For example: Trade Price = Number of Cotracts = 100 Ed of Day Settlemet Price = Variatio Margi o Positio = $3, (1.5pts x AUD24.66 x 100 cotracts) The cash rate futures cotract gives a exposure to AUD3,000,000 per cotract. Hece, the cotract value of a positio i the 30 Day Iterbak Cash Rate Futures is equivalet to the face value of the cotract multiplied by the umber of cotracts bought or sold. Physical 90 Day Bak Bills Ulike its best kow equivalet i the Uited States  the Eurodollar time deposit  the value of a physical 90 Day Bak Bill is calculated accordig to a yield to maturity formula that discouts the face value to establish the appropriate iterest cost over the 90 days.
2 The formula for the preset value (P) of a bak bill is: P = FaceValue 365 yield Days to Maturity 100 The face value represets the bill's future value, i.e. its value at the ed of its 90 day term. Please ote the Australia covetio is to use a 365 rather tha a 360 day year. I order to calculate the preset value (P) of a 90 Day Bak Bill which has a face value of $100,000 ad is tradig at a yield to maturity of 5.50%, the followig calculatios are performed: 100, P = = $98, This same formula ca be applied to value Bak Bills with varyig maturities (i.e. 30, 60, 90, 180 days) ad face values (i.e. $100,000, $500,000, $1,000,000). These values would simply be iserted ito the formula where appropriate. SFE 90 Day Bak Bills For SFE 90 Day Bak Bill Futures, where the cotract value is always $1,000,000, ad the term to maturity is exactly 90 days, the bak bill formula ca be rewritte as: P = 1,000, yield where the yield is the futures price deducted from 100. Therefore if a Bak Bill futures cotract was tradig at (ie. a yield of 5%) the value of the cotract would be: 1,000, P = = $987, SFE 90 Day Bak Bill Futures Tick Value Calculatios The dollar value of a 0.01% chage i yield does ot remai costat but rather varies i accordace with chages i the uderlyig iterest rate. Accordigly, to establish what the dollar value of a futures tick will be at a give price, the followig calculatios are made: 1. Use the cotract valuatio formula (as described above) to calculate the uderlyig value of the cotract at the omiated futures price. 2. Apply the same formula to that same futures price mius 0.01 (i.e., icrease the yield by 0.01%). 3. The differece betwee the two cotract values represets the dollar value of the tick at the omiated futures price. To determie the dollar value of a 0.01% chage i yield of a Bak Bill futures cotract which is tradig at a price of (ie. a yield of 5.00%) the followig calculatios are performed: 1. Futures cotract value at (5.00%)= $987, (rouded to two decimal places) 2. Futures cotract value at (5.01%)= $987, (rouded to two decimal places) 3. Differece (value of 0.01% of premium)= $24.06
3 SFE 90 Day Bak Bill Optios Premiums for optios o 90 Day Bak Bill futures are quoted i terms of aual percetage yield (e.g. 0.60% pa or 1.05% pa) with the value of a sigle poit of premium (ie. 0.01% pa) calculated by comparig its cotract value at the exercise price (expressed as 100 mius aual yield) ad its value at that same exercise price less oe poit (0.01%). For example, a 90 Day Bak Bill optio with a exercise price of ad a premium of 0.065% pa would be valued as follows: 1. Futures cotract value at (5.00%)= $987, (rouded to two decimal places) 2. Futures cotract value at (5.01%)= $987, (rouded to two decimal places) 3. Differece (value of 0.01% of premium)= $24.06 Sice we have 6.5 poits of premium, the fial premium i dollars is $ To exactly match the premium i dollars as calculated by SFE Clearig the premium should be calculated i the followig maer: $24.06 x = (rouded to four decimal places) x 100 = $ A fial importat poit to ote is that, for a optio with a particular exercise price, the value of 0.01% of premium is costat, while the tick value of the uderlyig futures cotract is variable with the level of iterest rates. To put it aother way, the value of a move of a certai size i the futures market will ot equate exactly i dollar terms with a move of the same size i the optio premium. Ivestors should also be cautious about implemetig coversio strategies owig to the differeces i tick sizes betwee a optio strike price ad the prevailig futures price. For example, it ca happe that a optio appears to be priced slightly below its itrisic value i terms of the yield whe i fact, i dollar terms, the pricig is correct. Australia Commowealth Treasury Bods The formula for calculatig the price per A$100 of a Australia Commowealth Treasury Bod as supplied by the Reserve Bak of Australia is: where v = 1/(1+i) where i is the aual percetage yield divided by 200. f = the umber of days from the date of settlemet to the ext iterest paymet date d = the umber of days i the half year edig o the ext iterest paymet date c = the amout of iterest paymet (if ay) per $100 face value at the ext iterest paymet date g = the fixed halfyearly iterest rate payable (equal to the aual fixed rate divided by 2). = the umber of full halfyears betwee the ext iterest paymet date ad the date of maturity (equal to 2 times the umber of years util maturity) a = v + v +.+ v = (1 v )/i The covetio adopted with Commowealth Treasury Bods is that iterest is paid o the fifteeth day of the appropriate moth with the last iterest paymet made at maturity. Usig the Reserve Bak pricig formula, the calculatios which would be performed to value a Commowealth Treasury Bod with a maturity of 15 October 2007, a coupo rate of 10.00%, a market yield of 5.70% ad a settlemet day of 7 April 1998 would be: i = v = f = (2/4/98 + T3 busiess (7/04/98) to 15/4/98) = 8 d = 182 g = 5
4 = 20 f/d = c = 5 Usig the above iputs, the bod would have a value of A$ per $100 face value (iclusive of accrued iterest). SFE 10 Year Treasury Bod Futures For SFE Treasury Bod futures, the pricig formula ca be simplified because there is always a exact umber of half years to maturity ad hece there is o requiremet to calculate accrued iterest. The formula for the value (P) of a 10 Year Bod futures cotract o SFE is writte as: 20 ( 1 v ) c P = v i 20 where: i = yield % pa divided by 200 v = 1/(1+i) = 20 c = coupo rate/2 Thus to value a 6% coupo 10 Year Treasury Bod cotract which is tradig at a price of (i.e. A yield of 4.50% pa.), the iputs would be: i = v = = 20 c = 3 Whe these iputs are icluded i the formula, the cotract value for the above cotract will be A$111, Note that the mathematical covetio is that multiplicatio ad divisio take precedece over, additio ad subtractio. I the futures formula, this meas that the divisio by i is performed before the additio of 100v 20. To exactly match the cotract value as calculated by SFE Clearig, steps C, D ad G must be rouded to exactly eight decimal places, with 0.5 beig rouded up. No other steps are rouded except K, which is rouded to two decimal places. SFE Clearig makes the calculatio i the followig maer: Futures Price A price B I = A/ C v = 1/(1 + B) D v E 1  v 20 = 1  D F 3(1  v 20 ) = 3 x E G 3(1  v 20 )/i = F/B H 100v 20 = 100 x D I G + H J I x 1,000 $111, K Rouded $111, SFE 10 Year Treasury Bod Futures Tick Value Calculatios The methodology used to calculate tick values for the 10 Year Treasury Bod Futures is idetical to that outlied i the previous example for 90 Day Bak Bill Futures.
5 For example, to determie the dollar value of a 0.01% chage i yield o a 10 Year Bod cotract tradig at a price of (ie. A yield of 5.64%), the followig calculatios are performed. 1. Futures cotract value at (5.64%) = $102, Futures cotract value at (5.65%) = $102, Differece (value of 0.01% of premium) = $ or $76.87 rouded to two decimal places. SFE 10 Year Treasury Bod Optios Like Bak Bill optios, 10 Year bod optios are quoted i terms of aual percetage yield (e.g % or 0.525%), with the value of a sigle poit of premium (ie. 0.01%) calculated as the differece betwee the cotract value at the exercise price (expressed as 100 mius the aual yield) ad its value at that exercise price less oe poit (0.01%). Please ote that whe makig these calculatios, cotract values are ot rouded to the earest cet before calculatig this differece. Accordigly, the dollar value of a optio o a 10 Year Treasury bod optio with a exercise price of ad a premium of 0.140% would be calculated as follows: 1. Futures cotract value at = $100, Futures cotract value at = $99, Differece (value 0.01% of premium) = $ Sice there is 14 poits of premium, the fial premium i dollars is calculated as: $ x 14 = $1, which whe rouded to the earest cet gives $ SFE 3 Year Treasury Bod Futures Tick Value Calculatios For SFE Treasury Bod futures, the Reserve Bak of Australia govermet bod pricig formula ca be simplified because there is always a exact umber of half years to maturity ad hece there is o requiremet to calculate accrued iterest. The formula for the value (P) of a 3 Year Bod Futures cotract o SFE is writte as: 6 ( 1 v ) c P = v i 6 where: i = yield % pa divided by 200 v = 1/(1+i) = umber of coupo paymets. For the 3 Year cotract this is 6. c = coupo rate/2 Thus to value a 6% coupo 3 Year Treasury Bod cotract which is tradig at a price of (i.e. a yield of 4.495% pa.), the iputs would be: i = v = = 6 c = 3 Whe these iputs are icluded i the formula, the cotract value for the above cotract will be A$104, Note that the mathematical covetio is that multiplicatio ad divisio take precedece over, additio ad subtractio. I the futures formula, this meas that the divisio by i is performed before the additio of 100v 6. To exactly match the cotract value as calculated by SFE Clearig, steps C, D ad G must be rouded to exactly eight decimal places, with 0.5 beig rouded up. No other steps are rouded except K, which is rouded to two decimal places. SFE Clearig makes the calculatio i the followig maer:
6 Futures Price A price B I = A/ C v = 1/(1 + B) D V E 1 v 6 = 1  D F 3(1 v 6 ) = 3 x E G 3(1 v 6 )/i = F/B H 100v 6 = 100 x D I G + H J I x 1,000 $104, K Rouded $104, Determiig Variatio Margis for 3 Year Treasury Bod Futures SFE Clearig determies the variatio or marked to market margi for variable tick cotracts i the followig by comparig the cotract value for the previous ed of day price (or the trade price if the cotract was bought or sold that day) ad that day's ed of day settlemet price or exit price. For example: 1. Bought 10 3 Year Treasury Bod Futures at price of (yield = 4.495%). The cotract value determied usig the bod formula is $104, per cotract. The cotract value for 10 cotracts is $1,041, Ed of day settlemet price for 3 Year Treasury Bod Futures is (yield = 5.510%). The cotract value is $101, x 10 cotracts = $1,013, Variatio Margi, determied by calculatig the differece betwee the two cotract values, that is, $1,041, $1,013, = $28, The margi paymet made o the 10 lot positio is $28, Calculatig the Tick Value for SFE 3 Year Treasury Bod Futures The dollar value of a 0.010% chage i yield does ot remai costat but rather varies i accordace with chages i the uderlyig iterest rate. Accordigly, to establish what the dollar value of a futures tick will be at a give price, the followig calculatios are made: 4. Use the cotract valuatio formula (as described above) to calculate the uderlyig value of the cotract at the omiated futures price. 5. Apply the same formula to that same futures price mius (i.e., icrease the yield by 0.010%). 6. The differece betwee the two cotract values represets the dollar value of the tick at the omiated futures price. For example, to calculate the dollar value of a 0.010% chage i yield whe the 6% coupo 3 Year cotract is tradig at a price of (i.e. a yield of 5.240%), the followig calculatios are performed. 1. Futures cotract value at (5.240%) = $102, Futures cotract value at (5.250%) = $102, Differece (value 0.01% of premium) = $ Which whe rouded to the earest cet gives $27.77 SFE 3 Year Bod Optios Premiums for the 3 Year Bod optios are calculated i exactly the same way as for 10 Year Bod optios, by referece to the value of a oepoit move i the uderlyig futures cotract from the exercise price to the exercise price less oe poit.
7 To value a 6% coupo 3 Year Treasury Bod optio which has a strike price of ad a premium of poits, the followig calculatios are made: 1. Futures cotract value at = $101, Futures cotract value at = $101, Differece (value 0.010% of premium) = $ Sice there is 24 poits of premium, the fial premium i dollars is calculated as: $ x 24 = $ which whe rouded to the earest cet gives $ A fial importat poit to ote is that, for a optio with a particular exercise price, the value of 0.010% of premium is costat, while the tick value of the uderlyig futures cotract is variable with the level of iterest rates. To put it aother way, the value of a move of a certai size i the futures market will ot equate exactly i dollar terms with a move of the same size i the optio premium. Ivestors should also be cautious about implemetig coversio strategies owig to the differeces i tick sizes betwee a optio strike price ad the prevailig futures price. For example, it ca happe that a optio appears to be priced slightly below its itrisic value i terms of the yield whe i fact, i dollar terms, the pricig is correct. 3 Year ad 10 Year Iterest Rate Swap Futures The cotract value formula for Iterest Rate Swap Futures is a modified versio of the Treasury Bod Futures pricig formula. The differece betwee the two formulas is the coupo rate. Iterest Rate Swap Futures have a coupo rate of 6.5% as opposed to the 6% used for Treasury Bod Futures. 3 Year Iterest Rate Swap Futures The formula for the value (P) of 3 Year Iterest Rate Swap Futures at SFE is writte as: ( 1 v ) c P = v i where: i = yield % pa divided by 200 v = 1/(1+i) = the umber of coupo paymets c = coupo rate/2 Thus to value a 6.5% coupo 3 Year Iterest Rate Swap Futures cotract which is tradig at a price of (ie. a yield of 5.70% pa.), the iputs would be: i = v = = 6 c = 3.25 Whe these iputs are icluded i the formula, the cotract value for the above cotract will be A$102, Note that the mathematical covetio is that multiplicatio ad divisio take precedece over, additio ad subtractio. I the futures formula, this meas that the divisio by i is performed before the additio of 100v 6. To exactly match the cotract value as calculated by SFE Clearig Corporatio (SFECC), steps C, D ad G must be rouded to exactly eight decimal places, with 0.5 beig rouded up. No other steps are rouded except K, which is rouded to 2 decimal places. The SFECC makes the calculatio i the followig maer: Futures Price A 100 price 5.70 B i = A/
8 C v = 1/(1 + B) D v E 1 v 6 = 1  D F 3.25(1 v 6 ) = 3.25 x E G 3.25(1 v 6 )/i = F/B H 100v 6 = 100 x D I G + H J I x 1,000 $102, K Rouded $102, Year Iterest Rate Swap Futures The formula for the value (P) of 10 Year Iterest Rate Swap Futures at SFE is writte as: ( 1 v ) c P = v i where: i = yield % pa divided by 200 v = 1/(1+i) = the umber of coupo paymets c = coupo rate/2 Thus to value a 6.5% coupo 10 Year Iterest Rate Swap Futures cotract which is tradig at a price of (ie. a yield of 4.500% pa.), the iputs would be: i = v = = 20 c = 3.25 Whe these iputs are icluded i the formula, the cotract value for the above cotract will be A$115, Note that the mathematical covetio is that multiplicatio ad divisio take precedece over, additio ad subtractio. I the futures formula, this meas that the divisio by i is performed before the additio of 100v 20. To exactly match the cotract value as calculated by SFE Clearig Corporatio (SFECC), steps C, D ad G must be rouded to exactly eight decimal places, with 0.5 beig rouded up. No other steps are rouded except K, which is rouded to 2 decimal places. The SFECC makes the calculatio i the followig maer: Futures Price A 100 price B i = A/ C v = 1/(1 + B) D v E 1  v 20 = 1  D F 3.25(1  v 20 ) = 3.25 x E G 3.25(1  v 20 )/i = F/B H 100v 20 = 100 x D I G + H J I x 1,000 $115, K Rouded $115,963.71
9 This documet was prepared by the Busiess Developmet Group of the Sydey Futures Exchage. SFE takes o resposibility for errors or omissios or losses arisig from actios based o this iformatio. This documet does ot substitute for the SFE Busiess Rules ad i the case of icosistecy, the Busiess Rules prevail. For further iformatio o SFE, or its products, please cotact the Busiess Developmet Group. Copyright Sydey Futures Exchage Limited 1998 Last Updated December 2005
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