能用画图法说明吗？谢谢

NO.PZ2024061801000032

问题如下：

A bond pays a semiannual coupon of $40 and has a current value of $1,109. The next payment on the bond is in four months, and the annual interest rate is 6.50%. Using an annual compounding assumption, the price of a six-month forward contract on this

bond is closest to:

选项：

$1,103.

$1,104.

$1,145.

$1,185.

解释：

Use the formula F = (S − I) × (1 + r)T, where I is the present value of $40 to be received in 4 months, or 0.333 years. At a discount rate of 6.50%:

I = $40 / 1.0650.333 = $39.17

F = ($1,109 − 39.17) × 1.0650.5 = $1,104.05

能用画图法说明吗？谢谢

按照6个月来画图，现在相当于t=2，T=6。那么40的coupon应该减去吗？

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1 个答案

李坏_品职助教 · 2025年02月22日

嗨，爱思考的PZer你好：

4个月的时候有40美元的coupon，折现到现在（0时刻）的现值 I = 40/[(1+6.5%) ^4/12] = 39.17

在0时刻，1109 - 39.17，然后一起复利计算到t=6时刻，F=(1109 - 39.17) * （1+6.5%）^6/12 = 1104.05

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NO.PZ2024061801000032 问题如下 A bonpays a semiannucoupon of $40 anha current value of $1,109. The next payment on the bonis in four months, anthe annuinterest rate is 6.50%. Using annucompounng assumption, the priof a six-month forwarcontraon thisbonis closest to: A.$1,103. B.$1,104. $1,145. $1,185. Use the formula F = (S − I) × (1 + r)T, where I is the present value of $40 to receivein 4 months, or 0.333 years. a scount rate of 6.50%: I = $40 / 1.0650.333 = $39.17F = ($1,109 − 39.17) × 1.0650.5 = $1,104.05 年化利率是6.5%，那么6个月的时间折现，折现时为什么不用（1+6.5%/2）的0.5次方呢？

2025-02-22 17:15 1 · 回答