The forward rate fit1,t2) of a bond, is the implicit interest rate in a future period between time t1 and t2. For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-rt1), and from period 0 to 12 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) exp(-r t2)). Suppose we observe the prices of a 14-year zero-coupon bond (with a face value of $93.31), where P(t1,t2) regans the price of the bond between 11 and 12, and a year 7-to-14 forward rate as follows:P(0.14) - $86.5496905000 and f(7,14) - 0.6074704253 %. Calculate the price of a 7-year zero-coupon, with face value $99.27: $82.9604 $96.0778 ✓(25 %) $96.2349 $82.1804
The forward rate fit1,t2) of a bond, is the implicit interest rate in a future period between time t1 and t2. For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-rt1), and from period 0 to 12 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) exp(-r t2)). Suppose we observe the prices of a 14-year zero-coupon bond (with a face value of $93.31), where P(t1,t2) regans the price of the bond between 11 and 12, and a year 7-to-14 forward rate as follows:P(0.14) - $86.5496905000 and f(7,14) - 0.6074704253 %. Calculate the price of a 7-year zero-coupon, with face value $99.27: $82.9604 $96.0778 ✓(25 %) $96.2349 $82.1804
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![The forward rate f(t1,12) of a bond, is the implicit interest rate in a future period between time t1 and t2.
For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-r t1), and
from period 0 to 12 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the
following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) exp(-r t2)). Suppose we observe the prices of a
14-year zero-coupon bond (with a face value of $93.31), where P(t1,t2) regans the price of the bond
between t1 and 12, and a year 7-to-14 forward rate as follows:P(0.14) - $86.5496905000 and f(7,14) -
0.6074704253 %. Calculate the price of a 7-year zero-coupon, with face value $99.27:
$82.9604
$96.0778
✓(25 %) $96.2349
$82.1804](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2544b074-24fb-4c8c-9c46-194a4d33d8d8%2Fc2224382-8375-4c4a-a560-81e94ba5396f%2Fezlwgsi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The forward rate f(t1,12) of a bond, is the implicit interest rate in a future period between time t1 and t2.
For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-r t1), and
from period 0 to 12 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the
following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) exp(-r t2)). Suppose we observe the prices of a
14-year zero-coupon bond (with a face value of $93.31), where P(t1,t2) regans the price of the bond
between t1 and 12, and a year 7-to-14 forward rate as follows:P(0.14) - $86.5496905000 and f(7,14) -
0.6074704253 %. Calculate the price of a 7-year zero-coupon, with face value $99.27:
$82.9604
$96.0778
✓(25 %) $96.2349
$82.1804
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