北美精算师fm教材financialmathematics习题答案第八章.pdf

《北美精算师fm教材financialmathematics习题答案第八章.pdf》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、FinancialMathematicsSecondEditionAPracticalGuideforActuariesandotherBusinessProfessionalsByChrisRuckman,FSA&JoeFrancis,FSA,CFAPublishedbyBPPProfessionalEducationSolutionstopracticequestions–Chapter8Solution8.1Thepriceofthebondsisfoundbyusingeachbond’syi

2、eldtofindthepresentvalueofthebond’scashflows:CFtP=∑t()1+yThepriceofthe1-yearbondis:110P==$101.85191.08Thepriceofthe2-yearbondis:4104P=+=$91.23891.089791.089792Thepriceofthe3-yearbondis:2020120P=++=$125.50851.097821.09782231.09782Solution8.2Thepriceisthe

3、sumofthepresentvaluesofthecashflows:CFt1515115P==∑++=118.6593()1+st1.071.06231.08tThepriceofthebondis$118.66.1FinancialMathematicsSolutionstopracticequestions–Chapter8Solution8.3WecalculatedthepricesinSolution8.1,sotheyieldtablewiththepricesis:MaturityA

4、nnualcouponPriceAnnualeffectiveyield110.000%101.85198.000%24.000%91.23898.979%320.000%125.50859.782%Weusethefollowingformulatofindthespotrates:CFtP=∑t()1+stSincethe1-yearbondhasonlyonecashflow,itsyieldisequaltotheone-yearspotrate:s1=8.000%Pluggings1into

5、theformulaforthepriceofthe2-yearbond,wesolvefors2:410491.2389=+2⇒=s29.000%1.08(1+s)2Pluggings1ands2intotheformulaforthepriceofthe3-yearbond,wesolvefors3:2020120125.5085=+23+⇒=s310.000%1.08(1.09)(1+s)3Solution8.4Thepriceper$100ofparvalueofthe5-yearbondth

6、atpays$7.50peryearis:CFt100Pa==+=∑t7.557.664%599.3394()1+y1.07664Butwecannotuseatovaluetheannuity-immediateconsistingof$40paidfor5years,becausetheyield57.664%of7.664%isonlyappropriateforthebondwith7.5%coupons.Weusethe5-yearspotratetofindthevalueof$100in

7、5years:100Presentvalueof$100paidin5years==$68.058351.08Subtractingthepresentvalueof$100payablein5yearsfromthevalueofthe7.5%5-yearbond,weareleftwiththevalueofastreamof5annualpaymentsof$7.50each.Onceweknowthevalueof5annualpaymentsof$7.50each,itisasimplema

8、ttertoscalethatvalueinordertoarriveatthevalueof5annualpaymentsof$40each:Presentvalueof5annualpaymentsof7.50=99.339468.0583−=31.281031.2810Presentvalueof5annualpaymentsof1.00==4.17087.50Presentvalueof5annualpaymentsof40.00=×404.17