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## _-Derivatives - Matt Will

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Financial Engineering
Lecture 10
Futures Options
OverviewA Futures Contract on an OptionThe underlying asset is not a stockThe underlying asset is a futures contractCall Futures OptionLong Call = The right to long a futures contractShort Call = The obligation to short a futures contractPut Futures OptionLong Put = The right to short a futures contractShort Put = The obligation to long a futures contract
Futures Options
Option SpecificationsFutures Options = FONo delivery occursCommodities are Settled in CashFinancials might take deliveryOne option = one futures contractExpirationFinancial optionsSame date as futures contract expirationCommodity OptionsExpire the month prior to the futures contract expiration
PricingFO prices are listed in “units”Each “Unit” has a \$ valueExample (Corn FO)Underlying asset = 5,000 bushels of cornPrice quoted in cents per bushel1 unit = \$501/8 of a unit = \$6.25 (on 1/8 cents per bushel)May 3600 Call = 20’320x\$50 + 3x\$6.25 = \$1,018.75The strike of 3600 = \$3.60 or 360 cents per bushelCME lists details
Futures Options
Example (Soybean FO)September soybean futures are selling for 1049 cents per bushelThe underlying asset is one futures contract on 5,000 bushels of soybeans as listed on the CBOTThe value of one futures contract5000 x \$10.49 = \$52,450The unit value is \$50Determined 5000 x .01 = \$50The futures option price is quoted in Units and ticks(ticks are 1/8 cents per bushel or \$6.25)But the total price is (\$50 x cents + \$6.25 x ticks)
Futures Options
Example (Soybean FO) - continuedSept1040P = 42’2 total cost=(\$50x42)+(\$6.25x2) = \$2,106.50Sept1040C = 53’2 \$2,565.50Sept1120C = 26’4 \$1,325.00BE Soybean Price on Sept1120C= 1120 + 26’4 = \$11.465 per bushelBE Contract Value on Sept1120C = \$56,000 +\$1325 = \$57,325.00
Futures Options
UnitsVary depending on the underlying assetEach asset has a unique relationship amongAsset priceFutures Contract specsOptionBasic Underlying Asset CategoriesCommodityFinancialCurrencyothers
Futures Options
Example - gold is quoted in \$ per ounceExample - Sugar is quoted in cents per poundCBOT web sitePricing – Same as regular options.Black ScholesBinomial
Futures Options
FO MarginDetermined by volatility and risk of lossFutures Options use unique margin accountingSPAN= Standard Portfolio ANalysis of RiskFutures Options UsesSame as futures w/ flexibilityFloors, ceilings, spreads, etcEmploys all Option strategiesArbitrage (lots of mispricing)
Futures Options
SWAPS
Birth 1981Definition - An agreement between two firms, in which each firm agrees to exchange the “interest rate characteristics” of two different financial instruments of identical principalKey pointsSpread inefficienciesSame notation principalOnly interest exchanged
SWAPS
“Plain Vanilla Swap” - (generic swap)fixed rate payerfloating rate payercounterpartiessettlement datetrade dateeffective datetermsSwap Gain = fixed spread - floating spread
SWAPS
Example (vanilla/annually settled)XYZ ABCfixed rate 10% 11.5%floating rate libor + .25 libor + .50Q: if libor = 7%, what swap can be made 7 what is the profit (assume \$1mil face value loans)A:XYZ borrows \$1mil @ 10% fixedABC borrows \$1mil @ 7.5% floatingXYZ pays floating @ 7.25%ABC pays fixed @ 10.50%
SWAPS
Example - contBenefit to XYZ Net positionfloating +7.25 -7.25 0fixed +10.50 -10.00 +.50Net gain +.50%Benefit ABC Net Positionfloating +7.25 - 7.50 -.25fixed -10.50 + 11.50 +1.00net gain +.75%
SWAPS
Example - contSettlement dateABC pmt 10.50 x 1mil = 105,000XYZ pmt 7.25 x 1mil = 72,500net cash pmt by ABC = 32,500ifliborrises to 9%settlement dateABC pmt 10.50 x 1mil = 105,000XYZ pmt 9.25 x 1mil = 92,500net cash pmt by ABC = 12,500
SWAPS
transactionsrarely done directbanks = middlemanbank profit = part of “swap gain”example - same continuedXYZ & ABC go to bank separatelyXYZ term = SWAP floating @ libor + .25 for fixed @ 10.50ABC terms = swap floating libor + .25 for fixed 10.75
SWAPS
Example - contsettlement date - XYZBank pmt 10.50 x 1mil = 105,000XYZ pmt 7.25 x 1mil = 72,500net Bank pmt to XYZ = 32,500settlement date - ABCBank pmt 7.25 x 1mil = 72,500ABC pmt 10.75 x 1mil = 107,500net ABC pmt to bank = 35,000bank “swap gain” = +35,000 - 32,500 = +2,500
SWAPS
Example - contbenefit to XYZfloating 7.25 - 7.25 = 0fixed 10.50 - 10.00 = +.50 net gain .50benefit to ABCfloating 7.25 - 7.50 = - .25fixed -10.75 + 11.50 = + .75 net gain .50benefit to bankfloating +7.25 - 7.25 = 0fixed 10.75 - 10.50 = +.25 net gain +.25total benefit = 12,500 (same as w/o bank)
Currency Swaps
Similar to interest rate swapsSame type loan, just diff currencyWHY?example:you have an investment in JapanProject is financed with US bondsYou look for SWAP partner so you can emulate holding Japanese bondsJava Yahoo principalYen loan 11% 12% \$ 1 mil\$ loan 8% 11.1% or Y120
Currency Swaps
example - continuedJava borrows \$1mil @ 8%Yahoo borrows Y120mil @ 12%Intl. Bank arranges swapJava swaps 8% \$ loan for 10.3% yen loan w/bankYahoo swaps 12% yen loan for 10.4% \$ loan w/banktotal available benefit = (11.1-8) - (12-11) = 2.1%
Currency Swaps
example - continuedbenefit to Java\$ loan +8 - 8 = 0Yen loan +11 - 10.3 = .7 net gain = +.7%benefit to Yahoo\$ loan 11.1 - 10.4 = +.7yen loan -12 + 12 = 0 net gain = + .7%benefit to bank\$ loan +10.4 - 8 = +2.4yen loan - 12 + 10.3 = -1.7 net gain = + .7%

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