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比如世界 · 2020年03月11日

问一道题:NO.PZ2020011303000223

问题如下:

What is the effective duration and convexity of a three-year Treasury bond with a face value of 1 million and a coupon of 4% when the term structure is flat at 5%? Express interest rates in decimals and consider five-basis-point changes.

选项:

解释:

The value of the bond is 97.245937. When there is five-basis-point increase in all rates so that the term structure is flat at 5.05%, the value falls by 0.135287 to 97.110650. When there is a five-basis-point decrease in all rates so that the term structure is flat at 4.95%, the value rises by 0.135514 to 97.381452. The duration is

0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703

The convexity is

(97.110650+ 97.381452-2×97.245937)/(97.245937× 0.00052)=9.35

Note that even more decimal places than those indicated is necessary to provide this estimate of convexity.

The value of the bond is 97.245937这个是怎么计算出来的?对face value,par value,market value ,bond price,pv,fv这几个名词,在做题的时候很晕,不知道什么时候要计算什么,麻烦老师再帮忙讲解一下,谢谢。

1 个答案

小刘_品职助教 · 2020年03月12日

 同学你好,

这道题的债券价值是这样算的,因为对于美国债券来说,通常是半年付息一次,所以计算债券的时候可以如下按计算器:

N=3*2=6 I/Y=5/2=2.5 PMT=4/2=2 FV=100,按计算器PV=-97.2459

face value和 par value是指面值,一张债券面值多少钱的意思,一般都是100,就是一张债券值100块,这么理解就可以了。

market value是指债券的市价,因为随着市场收益率的变化,原来面值100的债券,有可能在市场上你只要花95或者要花105才能买到。

bond price 一般指债券发行的价格,在中国一般的债券发行价格都是100,所谓的平价发行,也有可能出现溢价或者折价的情况,因为票息和YTM之间的关系不同导致的。

PV基本可以和market value等价,在计算债券的时候,已知未来的现金流,倒算出现在的价值。

FV计算在债券计算中比较少见,因为债券在到期的时候会回归到面值100,所以不太需要用到这个。

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NO.PZ2020011303000223问题如下 Whis the effective ration anconvexity of a three-yeTreasury bonwith a favalue of 1 million ana coupon of 4% when the term structure is fl5%? Express interest rates in cimals anconsir five-basis-point changes. The value of the bonis 97.245937. When there is five-basis-point increase in all rates so ththe term structure is fl5.05%, the value falls 0.135287 to 97.110650. When there is a five-basis-point crease in all rates so ththe term structure is fl4.95%, the value rises 0.135514 to 97.381452. The ration is0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703The convexity is(97.110650+ 97.381452-2×97.245937)/(97.245937× 0.00052)=9.35Note theven more cimplaces ththose incateis necessary to provithis estimate of convexity. 题目问3年期的treasurybon面值=1m,coupon rate=4%,利率=5%,利率的期限结构是flat的。求这个债券的effective ration和convexity。利率的变动幅度是5bp。treasury bon般每半年付息一次。首先利用计算器求债券的价格V0PMT=100*4%/2=2,FV=100,I/Y=5%/2=2.5%,N=3*2=6,得PV=97.245937利率上升5bp时,债券价格V-PMT=100*4%/2=2,FV=100,I/Y=5.05%/2=2.525%,N=3*2=6,得PV=97.110650价格下降0.135287利率下降5bp时,债券价格V+PMT=100*4%/2=2,FV=100,I/Y=4.95%/2=2.475%,N=3*2=6,得PV=97.381452价格上升0.135514ration=0.5*(价格上升幅度+价格下降幅度)/(V0*2)0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703convexity=(V+ + V--2*V0)/(V0*利率变动^2)=(97.110650+97.381452-2×97.245937)/(97.245937× 0.00052 )=9.35 老师好,1、题目的FV明明是1million,也就是100万,为啥计算不用1000000,而用100?我计算的三个PV都是您的结果乘以10000。2、the ration is0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703,为什么用BV的增加值和减少值,即0.135287,0.135514,课程里给出的公式明明是债券价格,也就是BV-和BV+?

2024-07-17 22:11 3 · 回答

NO.PZ2020011303000223 问题如下 Whis the effective ration anconvexity of a three-yeTreasury bonwith a favalue of 1 million ana coupon of 4% when the term structure is fl5%? Express interest rates in cimals anconsir five-basis-point changes. The value of the bonis 97.245937. When there is five-basis-point increase in all rates so ththe term structure is fl5.05%, the value falls 0.135287 to 97.110650. When there is a five-basis-point crease in all rates so ththe term structure is fl4.95%, the value rises 0.135514 to 97.381452. The ration is0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703The convexity is(97.110650+ 97.381452-2×97.245937)/(97.245937× 0.00052)=9.35Note theven more cimplaces ththose incateis necessary to provithis estimate of convexity. 题目问3年期的treasurybon面值=1m,coupon rate=4%,利率=5%,利率的期限结构是flat的。求这个债券的effective ration和convexity。利率的变动幅度是5bp。treasury bon般每半年付息一次。首先利用计算器求债券的价格V0PMT=100*4%/2=2,FV=100,I/Y=5%/2=2.5%,N=3*2=6,得PV=97.245937利率上升5bp时,债券价格V-PMT=100*4%/2=2,FV=100,I/Y=5.05%/2=2.525%,N=3*2=6,得PV=97.110650价格下降0.135287利率下降5bp时,债券价格V+PMT=100*4%/2=2,FV=100,I/Y=4.95%/2=2.475%,N=3*2=6,得PV=97.381452价格上升0.135514ration=0.5*(价格上升幅度+价格下降幅度)/(V0*2)0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703convexity=(V+ + V--2*V0)/(V0*利率变动^2)=(97.110650+97.381452-2×97.245937)/(97.245937× 0.00052)=9.35 Whis the effective ration anconvexity of a three-yeTreasury bonwith a favalue of 1 million ana coupon of 4% when the term structure is fl5%? Express interest rates in cimals anconsir five-basis-point changes.解析The value of the bonis 97.245937. When there is five-basis-point increase in all rates so ththe term structure is fl5.05%, the value falls 0.135287 to 97.110650. When there is a five-basis-point crease in all rates so ththe term structure is fl4.95%, the value rises 0.135514 to 97.381452. The ration is0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703The convexity is(97.110650+ 97.381452-2×97.245937)/(97.245937× 0.00052)=9.35Note theven more cimplaces ththose incateis necessary to provi this estimate of convexity.解析中ration和convexity计算都是直接用5BP,但是计算债券价格时又是假设semi-annucoupon payment. 所以lta Y应该用2.5还是5bp呢?

2023-09-12 11:14 1 · 回答

NO.PZ2020011303000223问题如下 Whis the effective ration anconvexity of a three-yeTreasury bonwith a favalue of 1 million ana coupon of 4% when the term structure is fl5%? Express interest rates in cimals anconsir five-basis-point changes. The value of the bonis 97.245937. When there is five-basis-point increase in all rates so ththe term structure is fl5.05%, the value falls 0.135287 to 97.110650. When there is a five-basis-point crease in all rates so ththe term structure is fl4.95%, the value rises 0.135514 to 97.381452. The ration is0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703The convexity is(97.110650+ 97.381452-2×97.245937)/(97.245937× 0.00052)=9.35Note theven more cimplaces ththose incateis necessary to provithis estimate of convexity. 题目问3年期的treasurybon面值=1m,coupon rate=4%,利率=5%,利率的期限结构是flat的。求这个债券的effective ration和convexity。利率的变动幅度是5bp。treasury bon般每半年付息一次。首先利用计算器求债券的价格V0PMT=100*4%/2=20,FV=100,I/Y=5%/2=2.5%,N=3*2=6,得PV=97.245937利率上升5bp时,债券价格V-PMT=100*4%/2=20,FV=100,I/Y=5.05%/2=2.525%,N=3*2=6,得PV=97.110650价格下降0.135287利率下降5bp时,债券价格V+PMT=100*4%/2=20,FV=100,I/Y=4.95%/2=2.475%,N=3*2=6,得PV=97.381452价格上升0.135514ration=0.5*(价格上升幅度+价格下降幅度)/(V0*2)0.5×(0.135287+0.135514)/(97.245937×0.0005)=2.784703convexity=(V+ + V--2*V0)/(V0*利率变动^2)=(97.110650+97.381452-2×97.245937)/(97.245937× 0.00052)=9.35 请问,用PMT20,FV100,用2,5利率,六期这几个数字反复按计算器都等于196。实在不知错在哪了?都是这么按的,烦请示范一下,感谢

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2023-03-16 13:10 1 · 回答

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2022-06-02 13:08 1 · 回答