Clare · 2022年04月28日
NO.PZ2019052801000038
问题如下：
The price of a bond is $1,058, it has a coupon payment of $30 every six mouths, the last payment is three mouths ago. The continuous interest rate is 5%. Calculate the forward price of a 6-month forward contract on this bond:
选项：
A.$998.72.
B.$1,032.21.
C.$1,067.24.
D.$1054.41.
解释：
D is correct.
考点：远期合约定价
解析：
画图大法定起始的时候，是不是不一样？ 如果把第一次coupon作为起始，那就是2笔coupon，第一笔发生在0时刻，第二笔发生在6个月？
为什么就把当下算成0，last three months算成-3；
NO.PZ2019052801000038 问题如下 The priof a bonis $1,058, it ha coupon payment of $30 every six mouths, the last payment is three mouths ago. The continuous interest rate is 5%. Calculate the forwarpriof a 6-month forwarcontra on this bon A.$998.72. B.$1,032.21. C.$1,067.24. $1054.41. is correct.考点远期合约定价解析PV=30e−0.05×0.25=29.6273PV0=30e^{-0.05\times0.25}=29.6273\\PV=30e−0.05×0.25=29.6273FP = (S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41FP\;=\;(S_0-PV0)e^{rT}=(1058-29.6273)e^{0.05\times0.5}=1054.41FP=(S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41 这种题目用画图法怎么
NO.PZ2019052801000038 问题如下 The priof a bonis $1,058, it ha coupon payment of $30 every six mouths, the last payment is three mouths ago. The continuous interest rate is 5%. Calculate the forwarpriof a 6-month forwarcontra on this bon A.$998.72. B.$1,032.21. C.$1,067.24. $1054.41. is correct.考点远期合约定价解析PV=30e−0.05×0.25=29.6273PV0=30e^{-0.05\times0.25}=29.6273\\PV=30e−0.05×0.25=29.6273FP = (S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41FP\;=\;(S_0-PV0)e^{rT}=(1058-29.6273)e^{0.05\times0.5}=1054.41FP=(S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41 为什么在折现vin时候e的次方是-rt?
NO.PZ2019052801000038问题如下The priof a bonis $1,058, it ha coupon payment of $30 every six mouths, the last payment is three mouths ago. The continuous interest rate is 5%. Calculate the forwarpriof a 6-month forwarcontra on this bon A.$998.72.B.$1,032.21.C.$1,067.24.$1054.41.is correct.考点远期合约定价解析PV=30e−0.05×0.25=29.6273PV0=30e^{-0.05\times0.25}=29.6273\\PV=30e−0.05×0.25=29.6273FP = (S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41FP\;=\;(S_0-PV0)e^{rT}=(1058-29.6273)e^{0.05\times0.5}=1054.41FP=(S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41如题，请问是哪里看出来1058是干净的报价？
NO.PZ2019052801000038 问题如下 The priof a bonis $1,058, it ha coupon payment of $30 every six mouths, the last payment is three mouths ago. The continuous interest rate is 5%. Calculate the forwarpriof a 6-month forwarcontra on this bon A.$998.72. B.$1,032.21. C.$1,067.24. $1054.41. is correct.考点远期合约定价解析PV=30e−0.05×0.25=29.6273PV0=30e^{-0.05\times0.25}=29.6273\\PV=30e−0.05×0.25=29.6273FP = (S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41FP\;=\;(S_0-PV0)e^{rT}=(1058-29.6273)e^{0.05\times0.5}=1054.41FP=(S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41 请问是不是计算远期合约价格和期初价格的时候都不需要考虑long还是short？我记得老师讲课的时候，都是以long futures为例画图，因为FP为支出，所以cost要从FP的折现值里减掉；income为收入，所以要从PV里减掉，最后两个折现值在期初相等，算出FP。但如果是short futures，FP为收入，那是不是income要从FP的折现值里减掉，而cost要从PV里减掉呢？
NO.PZ2019052801000038 问题如下 The priof a bonis $1,058, it ha coupon payment of $30 every six mouths, the last payment is three mouths ago. The continuous interest rate is 5%. Calculate the forwarpriof a 6-month forwarcontra on this bon A.$998.72. B.$1,032.21. C.$1,067.24. $1054.41. is correct.考点远期合约定价解析PV=30e−0.05×0.25=29.6273PV0=30e^{-0.05\times0.25}=29.6273\\PV=30e−0.05×0.25=29.6273FP = (S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41FP\;=\;(S_0-PV0)e^{rT}=(1058-29.6273)e^{0.05\times0.5}=1054.41FP=(S0−PV)erT=(1058−29.6273)e0.05×0.5=1054.41 这个难道不是未来我会拿到的v吗？应该是收入啊？谢谢！
