Finance with Dr. John Elder
HW#3
Chapt 4 (Continuous Compounding) # 1,4,9
Chapt 4 (Interest Rate Markets - FRA) # 5,6,23
Some check answers:
Chapt 4
1. R
c
= 13.76%
4. with monthly compouding is 9.57%
9. R
c
= 14.91%
5a. f1,2 = 8.4% 5b. f2,3 8.8%
6. $893.56
12. YTM is 6.407% c.c.
23.
Value FRA = L(R
k
- R
f
)*(T
2
- T
1
)*exp(-R
2
T
2
) (recall payment structured as if in arrears!
= $1,000,000 * (0.06 - 0.0575)*0.5 * exp(-0.0494*2)
5. Here is a more detailed answer to #5:
Maturity (months)
Spot Rate cc
Forward Rate
3
8.0
6
8.2
8.4
exp(0.082*6/12) = exp(0.08*
3/12
)*exp(f
1,2
*3/12)
9
8.4
8.8
12
8.5
8.8
15
8.6
9.0
18
8.7
9.2
6. From 12-15 months, forward rate is 9.0% c.c. or 9.102% quarterly, using
Rm = m*(exp(R
c
/m) - 1) = 4*[exp(.09/4)-1) = 9.102%
Value FRA = L(R
k
- R
f
)*(T
2
- T
1
)*exp(-R
2
T
2
) (recall payment structured as if in arrears!
= $1,000,000 * (0.095 - 0.09102)*0.25 * exp(-0.086*15/12)
= 893.56