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VasicekVasicekVasicek1(Yield-Curve)(a)(b)(c)(b)(d)YTMTermStructureofInterestRate156SpotRateabcd10-12SpotRateForwardInterestRate10-111ThePureExpectationsTheory10-1(b)(c)2LiquidityTheoryLiquidityPremium3=+3PreferredHabitatTheory510510(BiasedExpectationsTheory)2MarketSegmentationTheory4()+×−=365DPVPVFVy÷−=51−×+=LPVCNMy+++++=1)/365()1()/365()1(fdfyfCfdfyfCPV1)/365()1(1)/365()1(−+++−+++nfdfyMnfdfyfC6VasicekVasicek19771rshortrateinstantaneousshortrateVasicekrLrrVASICEKTPYBAeP−=rTBTAY⎟⎠⎞⎜⎝⎛+⎟⎠⎞⎜⎝⎛−=SeBST−−=1SSLY+−=2∞22()2422SBσYTBA−−=∞P=(BondPrice)T=TimeToMaturity)r=ShortRateL=Long-RunMeanLeverS=SpeedOfAdjustmente==StandardDeviation=MarketPriceOfInterestRateRisk10-11Vasicek,Oldrich,AnEquilibriumCharacterizationoftheTermStructure,JournalofFinancialEconomics,Vol.5,No.2,(November1977),pp.177-188.7110.1200947210.1∑=+=niiirCFP1)1(PCFirExcelYield10-28910.2YIELDJ2=YIELD(H2,G2,E2,C2,100,1)YIELDPrJ210.23101234567101112131=(1-I11)*(J12-J11)/(I12-I11)+J11L210.310.3432dxcxbxaY+++=Y’Y-Y’ExcelabcdEXCEL1sheet3EXCEL10.41110.42Y’Y-Y’(Y-Y’)210.510.412310.51.610.510.6-1000010.6abcd10.5Y-Y’210.5abcd0.0096174510.004343999-0.000144208-0.000002717Y=0.009617451+0.004343999x--0.000144208x2--0.000002717x240.51510.171310.7VASICEKVASICEK21A1VasicekA3INPUTA4-C810.82A4-A8ShortRate(r)Long-RunMeanLever(L)SpeedOfAdjustment(S)StandardDeviation()MarketPriceOfInterestRateRisk(λ)10.83C4-C881011410C4-C85$C$4$C$5$C$6$C$7$C$8B4-B8=C4/200=C5/200=C6/100+0.01=C7/500=C8/100B4-B8rLS10.82EXCEL1410.8VASICEKINPUTSVASICEK1B10-B16Outputs:TimeToMaturity(T)Infinitely-LongRate(Y)BABondPrice(P)Y2B11:N11=1/12,=1/4,=1/2,1,2,3,4,5,10,15,20,25,30B12:N12=L-σ^2/(2*S^2)+(λ*σ)/SB13=(1-EXP(-S*B11))/SB13C13-N13B14=(B13-B11)*B12-(σ^2*B13^2)/(4*S^2)B14C14-N14B15=EXP(-S*B11B15C15-N15B16=(-B14)/B11+(B13/B11)*$B$4B16C16-N16136123451015202530Y10.910-9VASICEKOUTPUTS15ASICEKB12-N12CtrlB16-N16/XYE2-I1010.10sheet10.10sheet10.1110.11VasicekVasicekVasicek16YYYYYYYExcelsheet1sheet21970.1-2000.610.1210.121970.1-2000.61sheet119—214%11999119947sheet2sheet119—2117sheet1sheet2sheet2!A19=IF(LARGE((ROW($2:$500)*(ABS(Sheet2!$D$2:$D$500-$B$4)0.001)),ROW($A1))=0,,OFFSET(Sheet2!C$1:C$500,LARGE((ROW($2:$500)*(ABS(Sheet2!$D$2:$D$500-$B$4)0.001)),ROW($A1))-1,0,1,1))Ctrl+Shift+EnterA19B19=IF(LARGE((ROW($2:$500)*(ABS(Sheet2!$D$2:$D$500-$B$4)0.001)),ROW($A1))=0,,OFFSET(Sheet2!D$1:D$500,LARGE((ROW($2:$500)*(ABS(Sheet2!$D$2:$D$500-$B$4)0.001)),ROW($A1))-1,0,1,1))Ctrl+Shift+Enter10.1310.13Vasicek1819