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OOSTKSTKmax,010001691S-⎛⎝⎜⎞⎠⎟⎡⎣⎢⎤⎦⎥400.004,0001397.006006003,4002396.101807803,2203398.204203603,6404397.102205803,4205396.70806603,3408395.402609203,0809393.304201,3402,6601,34010393.60601,2804,06011391.803601,6403,70012392.701801,4603,88015387.001,1402,6002,7401,26016387.0002,6004,00017388.102202,3804,22018388.701202,2604,34019391.004601,8004,80022392.302601,5405,060247142463424914=-S2*()()FSFSS12222+-+-**()SF22*-()SS22-*()SF22*-()SS22-*NYMEXνσσρσσ=+-SFSFhh2222∂ν∂σρσσhhFSF=-222∂ν∂22/hhSF=ρσσ(.)210800320040064....×=064100000042000.,,,×=15.2ARmmm1+⎛⎝⎜⎞⎠⎟3.1ARnλ3.21001105201λ..=AARmRnmnλ112=+⎛⎝⎜⎞⎠⎟λRmRm112=+⎛⎝⎜⎞⎠⎟RmRm12133=+⎛⎝⎜⎞⎠⎟ln(.)()RmRm21134=-λ/(.)()4100808002λ..-=()FSrTt=-λ3.5()SrTtλ-()SrTtλ-()SrTtλ-()SrTtλ-()SFrTtλ--F==×404050005025λ...()KerTt--()fKeSrTt+=--()fSKerTt=---3.6()FSerTt=--fe=-=-×93095080805006...()()FSIerTt=--(.)37()()FSIerTt--()()SIerTt--()()FSIerTt---()()FSIerTt--()()SIeFrTt---Ieee=++=---0750750752162002004006.......()Fe=-=×502162511400808333....()fKeSIrTt+=---()fSIKerTt=----(.)38()()FSIerTt=--Iee=+=-×-60601116500905010....fe=--=--90011165910350501...eqTt--()fKeSerTtqTt+=----()()fSeKeqTtrTt=-----()()(.)39FSerqTt=--()()(.)310fee=-=--×-×2527118004050105.....fe==×25257600605...()fFKerTt=---()(.)311()fFKerTt---()()fFKerTt---()()fFKerTt---()()()()SFKSFKTT-+-=--()fFKerTt----()()fFKerTt---()()FKefrTt----()FSerqTt=--()()(.)312Fe==×40040503005025...FSerqTt--()()FSerqTt--()()FSerqTt--()()FSerqTt--()()SerqTt()()--Δ12=+aβΔaSS+βΔ2βSFNSF=β1.52,100,00021150000,ββ-*SFββ*S-FKe-r(T-t)e-r(T-t)ffKeSerTtrTtf+=----()()fSeKerTtrTtf=-----()()(.)313FSerrTtf=--()()(.)314F=Se3.15T-trFS+Ue3.16T-trFSe3.17r+uT-tU2e=1.865-0.07F=4501.865e=484.60.07FS+Ue3.18T-trFSUeT-t-rFS+Ue3.19r(T-t)(SU)er(T-t)FS+Uer(T-t)FS+Ue3.20r(T-t)FSe3.21(r+u)(T-t)FSer+uT-tFeS+UeyT-trT-tFeSeyT-tr+uT-tFSeruyTt=+--()()(.)322r-rfF=Se3.23cT-tF=Se3.24c-yT-t-Fe-rT-t+STST-+----FeESerTtTkTt()()()-+=----FeESerTtTkTt()()()0FESeTrkTt=--()(.)()()325STSTSTSTSTSTSTSTSTSTSTSTSTSKerTt---()SerTt()-SIKerTt----()()()SIerTt--SeKeqTtrTt-----()()SerqTt()()--Fieδe2δe3δeiδ(FFiiie--1)δ(FF(FFiiiniiineee--=---11))()δδδ(FFi=1niine--∑1)δ()()()[]()FFFFFFeFFennnnnnn-+-++-=----112100δδFnST()SFeTn-0δF0()FeSFeSenTnTn00δδδ+-=F0SeTnδG0G0enδSeTnδF0G0SeTnδF00=G3.5012n-1nF0F1F2Fn-1Fnee2e3en0/0(F1-F0)e2(F2-F1)e2(Fn-Fn-1)enn/0(F1-F0)en(F2-F1)en(Fn-Fn-1)en1001701052e.$123.×=10037010011ee..$123.=10001052e.×r*T*T*T*r=r4.1*)TrTTT**--T*r*∃r∃()***rrrrTTT=+--r*r*T*r*rTrT+∂∂412597501012ln...+⎛⎝⎜⎞⎠⎟=215194901047ln...+⎛⎝⎜⎞⎠⎟=ln..11090001054+⎛⎝⎜⎞⎠⎟=441049601047050105415eeeR-×--++=....eR-=15085196..()R=-=ln...085196150106866610610160104705010541001068152eeeeR-×-×-×-+++=.......5555180180101202501050507501061125010745175eeee-×-×-×-×+++=.........01081233.×+R()510581782225007213275eeRR-×+-×+=../..541815064×=$5.$1.98203271041001041593840140...ii+==∑71041001041637336036...ii+==∑1041.-()FSIerTt=--()4.2120601826121978+×=.658030334201e-×=...(121.978-5.803)e0.73970.1×=125094.1250946148183120242..-×=1202421400085887...=T*T*T*r*V*VerT***=-100V*erTFeeerTrTrTrT==--10010043****(.)FerTT=--100∃()*∃rT*1351054510901075%×-×=..r*-=1040000952101227.ln..∃r-=1024660969501256.ln..r*∃rrrTrTTT=--***∃()1227146125690561180%...×-×=360100nY()-2983659000828×=.0.0825230-0.081400.08649010097890086402466e-×=...ticiBceiinyti==-∑144(.)DtceBiiytini=-=∑145(.)DtceBiiniyti=⎡⎣⎢⎤⎦⎥=-∑1tititi∂∂Bycteiiytini=--=∑146(.)∂∂ByBD=-(.)47ΔΔByBD=-(.)48ΔΔBBDy=-5e=4.709-0.120.5×B-+BDyyΔ1DFDSΔΔS=-SD4.9SyΔΔFFDyF=-4.10NSDFDSF*.=411330000097360005025678,,,...×=y4.111000000093062506809207942,,,....×=∂∂2221Bycteiiytini=-=∑titititiBALibor9.95%BBABAABBALibor+1%10%Libor9.95%BALibor9.9%Libor10.0%BALibor9.9%Libor+1Libor10%10.0%100105.222-yr.TN30bps2.yr.TN38bps7.5233.yr.TN35bps3.yr.TN44bps7.7144-yr.TN38bps4-yr.TN48bps7.8355-yr.TN44bps4-yr.TN54bps7.9066-yr.TN48bps6-yr.TN60bps7.9477-yr.TN50bps7.yr.TN63bps7.971010-yr.TN60bps10-yr.TN75bps7.99ritiBKeQertrtiniiii11=+--=∑BQekertrt21111=+--*VBB=-21Beee102501075010512501144104=++-×-×-×......9824Bee2025010250151100=+-×-×.....10251()kRQeirtii--05.()*kkert--11()().*kkekRQertirtin-+---=∑1111052()().*kkeRQkertirtin-+---=∑1111052.....,...t-tt-t*2132...........RrtrtRrtrt2221133322075010502501005010751250110750105=-=×-×==-=×-×0501175..=R0.1104R0.121023()()4051400501104100400501210100427010250105075011125..(...).........-+-××+-××=--×-×-×eeeBA11%SterlingDollars8%Sterling12%12%SterlingDoiiars8%Dollars9.4%BA11%SterlingDollars8%Sterling12%12%SterlingDoiiars8%Dollars8.4%BA11%SterlingDollars9.0%Sterling12%12%SterlingDoiiars8%Dollars9.4%VSBBFD=-BeeeD=++=--×-×080810896400900920093......BFeee=++=--×-×6060126012305500400420043...123055110964155-=tiritiFititi()12141..Feirtii--()1015Fenrtnn--000909100096000909100100000909100106005100520053.........eee×××===(..).(..).(..)....600009608021600010108016600010608013009100920093×-=-×-=-×-=--×-×-×eee(.)().120000106102040093×-=-×e5218218STpXe-r(T-t)S-Xe-r(T-t)Se-Xe-r(T-t)=-=-201837101..Xe-r(T-t)c+Xe-r(T-t)ScS-Xe-r(T-t)cmax(S-Xe-r(T-t),)(.)071S-Xe-r(T-t)51-50e=$3.91-0.120.5Xe-r(T-t)-SXe-r(T