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mx · 2022年06月02日

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

  1. FRM I
  2. Valuation And Risk Models

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.

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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.

这个对应的公式是什么？

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品职答疑小助手雍 · 2022年06月02日

同学你好，effective duration的定义公式，0.5*（p+ + p-）/（p*△y）

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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

2023-03-29 17:24 2 · 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 答案给的公式是相加

2023-03-16 13:10 1 · 回答