债券凸度(德意志银行Excel金融工程建模)

1、债债券券凸凸度度基基础础年年比比例例利利率率（AnnualAnnual PercentagePercentage RateRate）说明：本模板用两种方法来计算凸度输输入入利率惯例:0 = APR，1=EAR0年息票率5.0%到期收益率9.0%年付息次数2距到期的时期数8面值（元）1000输输出出每期的贴现率4.5%每次支付的利息25.00用用现现金金流流计计算算债债券券凸凸度度第n期012345678时长（年）0.00.51.01.52.02.53.03.54.0小计现金流25.0025.0025.0025.0025.0025.0025.001025.00现金流的现值23.9222.8921

2、.9120.9620.0619.2018.37720.76868.08权重2.8%2.6%2.5%2.4%2.3%2.2%2.1%83.0%100.0%权重*（时长平方+时长）0.020.050.090.140.200.270.3316.6117.72凸度16.23用用公公式式计计算算债债券券凸凸度度凸度16.23债债券券凸凸度度用用凸凸度度计计算算价价格格敏敏感感性性年年比比例例利利率率（AnnualAnnual PercentagePercentage RateRate）输输入入利率惯例:0 = APR，1=EAR0年息票率5.0%到期收益率10.0%年付息次数2距到期的时期数8面值（元）

3、1000输输出出每期的贴现率5.0%每次支付的利息25.00图图形形输输出出到期收益率1.0%2.0%3.0%4.0%5.0%6.0%7.0%每期贴现率0.5%1.0%1.5%2.0%2.5%3.0%3.5%到期收益率的变动-9.0%-8.0%-7.0%-6.0%-5.0%-4.0%-3.0%债券价值11561115107510371000965931当前债券价格838838838838838838838债券价格的变动率37.9%33.0%28.2%23.6%19.3%15.1%11.1%修正的久期3.463.463.463.463.463.463.46用久期近似计算的价格变动率31.2%27

4、.7%24.3%20.8%17.3%13.9%10.4%凸度16.2316.2316.2316.2316.2316.2316.23用久期和凸度近似计算的价格变动率37.8%32.9%28.2%23.7%19.4%15.2%11.1%用用凸凸度度计计算算价价格格敏敏感感性性12.0%10.0%8.0%6.0%4.0%2.0%0.0%-2.0%-4.0%-6.0%-8.0%-10.0%-40%-30%-20%-10%0%10%20%30%40%50%到到期期收收益益率率变变动动率率价价格格变变动动率率债券价格的变动率用久期近似计算的价格变动率用久期和凸度近似计算的价格变动率8.0%9.0% 10.

5、0% 11.0%12.0%13.0%14.0%15.0%16.0%17.0%18.0%19.0%4.0%4.5%5.0%5.5%6.0%6.5%7.0%7.5%8.0%8.5%9.0%9.5%-2.0%-1.0%0.0%1.0%2.0%3.0%4.0%5.0%6.0%7.0%8.0%9.0%8998688388107837567317076846626406208388388388388388388388388388388388387.2%3.5%0.0%-3.4%-6.7%-9.8%-12.8%-15.7%-18.4%-21.1%-23.6%-26.1%3.463.463.463.463.4

6、63.463.463.463.463.463.463.466.9%3.5%0.0%-3.5%-6.9%-10.4%-13.9%-17.3%-20.8%-24.3%-27.7%-31.2%16.2316.2316.2316.2316.2316.2316.2316.2316.2316.2316.2316.237.3%3.5%0.0%-3.4%-6.6%-9.7%-12.6%-15.3%-17.9%-20.3%-22.5%-24.6%年年比比例例利利率率（AnnualAnnual PercentagePercentage RateRate）用用凸凸度度计计算算价价格格敏敏感感性性12.0%10.0%

7、8.0%6.0%4.0%2.0%0.0%-2.0%-4.0%-6.0%-8.0%-10.0%-40%-30%-20%-10%0%10%20%30%40%50%到到期期收收益益率率变变动动率率价价格格变变动动率率债券价格的变动率用久期近似计算的价格变动率用久期和凸度近似计算的价格变动率20.0%10.0%10.0%600838-28.5%3.46-34.6%16.23-26.5%债债券券凸凸度度动动态态图图实实际际年年利利率率（EffectiveEffective AnnualAnnual RateRate）输输入入利率惯例:0 = APR，1=EAR11年息票率5.0%10到期收益率9.5%1

8、9年付息次数22输输出出每期的贴现率4.6%动动态态图图输输出出到期时间(年）123456789距到期期数24681012141618附息票债券的凸度1.805.2210.0716.1723.3431.3940.1649.4859.21零息票债券的凸度1.835.4810.9618.2627.4038.3651.1465.7582.19债券凸度动态图3025201510500 100 200 300 400 500 600 700 800 900 到期时间（年）凸度101112131415161718192021222022242628303234363840424469.2079.3389.4999.57 109.50 119.18 128.58 137.63 146.29 154.55 162.37 169.74 176.67100.46 120.55 142.47 166.21 191.78 219.18 248.40 279.45 312.33 347.03 383.56 421.92 462.10实实际际年年利利率率（EffectiveEffective AnnualAnnual RateRate）债券凸度动态图3025201510500 100 200 300 400 500 600 700 800 900 到期时间（年）凸度2