ʱ : 金融工程习题 - 百度文库ϿʼĶ
2ȣ8.4%
3ȣ8.8% 4ȣ8.8% 5ȣ9.0% 6ȣ9.2%
10.ڻ۸=20e0.1?0.25=20.51Ԫ
11.ָڻ۸=10000e(0.1-0.05)?4/12=10125.78㡣 12.12º5ºɷ1ԪϢֵ=e-0.06?2/12+e-0.06?5/12=1.96Ԫ
Զڼ۸=(30-1.96)e0.06?0.5=28.89Ԫ
۸Զڼ۸ԶںԼijʼ۸Ϊ0
23º2ɷ1ԪϢֵ= e-0.06?2/12=0.99Ԫ Զڼ۸=35-0.99e0.06?3/12=34.52Ԫ
-0.063/12
ʱͷԶںԼֵ=28.89-34.52e?=-5.55Ԫ 13. 9´سɱֵ=0.5+0.5e-0.05?3/12+0.5e-0.05?6/12=1.48Ԫ Զڼ۸=(80+1.48)e0.05?9/12=84.59Ԫ
14. ڶʱɼٶͻѡĽڡǿԺ
֤ʸڱʣӵԶҶͷĿͻѡĽڣӵԶҿͷĿͻѡٵĽڡ෴ʵڱʣӵԶҶͷĿͻѡٵĽڣӵԶҿͷĿͻѡĽڡֻҪںԼЧУʺͱʵĸߵʹ䣬û⣬пɰԭۡ
ǵʺͱʽΪӽʱߵĸߵʹпܷ仯ˣͻѡڵȨرļֵӦֵ
ԼǩͻѡĽڣпһʡ
15. ֻеҵϵͳԷյ0ʱ˵ܳ
16. תʣΪ10.44%,ƽ
Ϊ1.98
аSԪ/˾1˾ƽ𣬰1.98Ļƽʴͻ1꣬ͬʱe0.0198˾1Զڻƽ𣬸ݻƽĴɱгʣǿƽ1Զڼ۸ΪSe0.0975Ԫ/˾Ҳ˵1յSe0.0198+0.0975=Se0.1173Ԫֽ𡣿ɼƽΪ11.73%Ȼƽʸ 17. ʿڻۼ۸Ϊ
0.65e0.1667(0.07-0.02)=0.06554
ɼʵʵڻ۸̫ˡͶ߿ͨԪʿɣʿڻ
18. 12ʵȼ۵3¼һθΪ 4e0.03-1=12.18% ˣÿӦõϢΪ
100.1218/43045.5Ԫ
19. ڹɼָϵͳԷΪ˹ɼָڻ۸ǵԤ
δֵָ
ģϰ⣺
1. A˾B˾ҪڽгϽ5ڱΪ2000ԪĴ֧ʷֱΪ
̶ A˾ 12.0 LIBOR+0.1% B˾ 13.4 LIBOR+0.6%
A˾ҪǸʴB˾Ҫǹ̶ʴһʻΪнõı0.1Ҫ˫ͬ
2. X˾ϣԹ̶ʽԪY˾ϣԹ̶ʽԪұüڻʼֵܽӽг˾ı£
Ԫ Ԫ X˾ 5.0 9.6% Y˾ 6.5 10.0%
һһΪнõı50㣬Ҫ˫ͬʷге
3. һݱΪ10Ԫʻ10µޡʻ涨6µLIBORʽ12ʣÿһθг϶Խ6µLIBORʵʵƽΪ10ǰ6µLIBORΪ9.6֧ʵһֵΪ٣̶֧ʵһֵΪ٣
4. һݻһ15µޡʻ涨ÿ꽻Ϊ14Ϊ2000ӢΪ10Ϊ3000ԪʽֽӢڵṹƽġʻǽǩģǽ8Ԫʽ11ӢʡڻΪ1Ӣ1.6500Ԫ֧ӢһֵΪ٣֧ԪһֵΪ٣
5. ͻгպ÷յ
6. X˾Y˾ĸгϵ10500ԪͶʿԻõΪ
̶ X˾ 8.0 LIBOR Y˾ 8.8 LIBOR
X˾ϣԹ̶ʽͶʣY˾ϣԸʽͶʡ
һʻΪнõı0.2Ҫ˫ͬ
7. A˾B˾ҪڽгϽ֧ʷֱΪ
A˾ B˾
Ԫ LIBOR0.5 LIBOR+1.0% Ԫ̶ 5.0 6.5%
A˾ҪԪʴB˾ҪǼԪ̶ʴһһϣлõ0.5˫ͬA˾B˾֧ôŵģ
8.Ϊʲô˵һԷֽΪһϵԶЭ飿
ϰ
1. A˾ڹ̶ʴгԵıȽƣA˾ǸʴB˾ڸʴгԵıȽƣA˾ǹ̶ʴΪṩ˻˾ڹ̶ʴϵ1.4%ڸʴϵ0.5˫ÿ潫1.4%0.5%=0.9%ΪҪ0.1%ı꣬A˾B˾ÿ˽0.4%档ζA˾B˾ֱLIBOR0.3%13%ʽʵЭ鰲ͼʾ
12.3% 12.4% 12% A н B LIBOR+0.6%
LIBOR LIBOR
2. X˾ԪгбȽƵԪY˾ԪгбȽƵԪΪṩ˻˾ԪϵΪ1.5%ԪϵΪ0.4%˫ڻеΪ1.5%0.4%=1.1%ΪҪȡ0.5%нѣX˾Y˾ֱ0.3%ĺ档X˾ʵ9.6%0.3%=9.3%ʽԪYʵ6.5%0.3%=6.2%ԪʵЭ鰲ͼʾеĻʷге
Ԫ5% Ԫ6.2% Ԫ5% A н B Ԫ10%
Ԫ9.3% Ԫ10%
3. Ŀṩ֪LIBORߵṹƽģ10%һθԼĹ̶ծȯļֵΪ
6e?0.3333?0.1?106e?0.8333?0.1?103.33Ԫ
ԼĸծȯļֵΪ
?100?4.8?e?0.3333?0.1?101.36Ԫ
ˣ֧ʵһļֵΪ103.33?101.36?1.97Ԫ̶֧ʵһļֵΪ1.97Ԫ
4.ǿԶںԼۡӢԪʷֱΪ10.437.703º15µԶڻʷֱ
1.65e?0.25?0.0273?1.63881.65e?1.25?0.0273?1.5946֧ӢһԶںԼ
ֵΪ
?3?2.8?1.6388?e?0.077?0.25??1.56Ԫ ?3?2.8?1.5946?e?0.077?1.25??1.33Ԫ
ӦԶںԼļֵΪ
?30?20?1.5946?e?0.077?1.25??4.61Ԫ
ԻԼļֵΪ?1.56?1.33?1.72?4.61Ԫ
5.÷ԴڽԷΥԼĿԣгԴʡʵгIJ
6.X˾ڹ̶ͶϵΪ0.8ڸͶϵΪ0˻0.80.2Ҫ֧УʣµXYÿ˸0.3仰˵X˾Ի8.3ĻرY˾ԻLIBOR0.3Ļرͼʾ
8.3% 8.5% LIBOR X н Y 8.8%
LIBOR LIBOR
7. A˾ڼԪ̶гбȽƣB˾ԪгбȽƣ˾ҪĽԼбȽƵһ֣˴ڻĻᡣ
˾Ԫʽϵ0.5%ڼԪ̶ʽϵ1.5%ߵIJ1%˺DZڵ1%100㣬нҪ50㣬AB˾ֱɵ25㡣˿һA˾LIBOR+0.25%ԪʣB˾6.25%ļԪ̶ʡ
Ԫ5% Ԫ6.25% Ԫ5% A н B ԪLIBOR+1%
ԪLIBOR+0.25% ԪLIBOR+1%
֧ڻʼʱͷָʾ෴ڻֹʱͷָʾͬнڴڼеգԶں