236 Mathematics for Finance
as follows:
B(0,1) = 0. 9901 ,
B(0,2) = 0. 9828 ,
B(0,3) = 0. 9726 ,B(1,2) = 0. 9947 ,
B(1,3) = 0. 9848 ,B(2,3) = 0. 9905.
The corresponding yields are
y(0,1)∼= 11 .94%,
y(0,2)∼= 10 .41%,
y(0,3)∼= 11 .11%,y(1,2)∼= 6 .38%,
y(1,3)∼= 9 .19%,y(2,3)∼= 11 .45%.The forward rates are
f(0,0)∼= 11 .94%,
f(0,1)∼= 8 .88%,
f(0,2)∼= 12 .52%,f(1,1)∼= 6 .38%,
f(1,2)∼= 12 .00%,f(2,2)∼= 11 .45%.We can read off the short rates and compute the values of the money market
account
r(0) =f(0,0)∼= 11 .94%,
r(1) =f(1,1)∼= 6 .38%,
r(2) =f(2,2)∼= 11 .45%,A(0) = 1,
A(1)∼= 1. 0100 ,
A(2)∼= 1. 0154 ,
A(3)∼= 1. 0251.
Exercise 10.21
Which bond prices in Example 10.13 can be altered so that the values
of the money market remain unchanged?Exercise 10.22
Using the data in Example 10.13, compare the logarithmic return on
an investment in the following securities over the period from 0 to 3:
a) zero-coupon bonds maturing at time 3; b) single-period zero-coupon
bonds; c) the money market account.