In this question, we investigate how to determine forward rates using the market

Question

In this question, we investigate how to determine forward rates using the market rate on a swap contract. Suppose that 6, 12, 18, and 24-month OIS rates are 3.7%, 4.1%, 4.3%, and 4.7%, respectively. 6-month LIBOR rate is 4%, and forward LIBOR rates for 6-12 and 12-18 months are 4.4% and 4.8%, respectively. OIS rates are continuously compounded and LIBOR rates are semiannually compounded (again, you will have no need to convert semiannual rates to continuous rates). The market rate is 4.5% for a two-year swap (negotiated today) to pay LIBOR A. Calculate the present value of the first three exchanges (6, 12, and 18 months) from the two-year swap. Assume that the swap is on a notional principal of $100 (make it simple). B. Note that the present value of the two-year swap must be zero. What should be the present value of the last exchange (24 months) from the swap? C. Determine the 6-month forward LIBOR rate (per annum) for 18-24 months.

Explanation / Answer

1. 12 month libor = r

(1+r/2)^2 = (1+4%/2)*(1+4.4%/2)

r = 4.2%

18 month libor = s

(1+s/2)^3 = (1+4%/2)*(1+4.4%/2)*(1+4.8%/2)

s = 4.4%

Exchange values for first 3:

4-3.7, 4.2-4.1, 4.4-4.3

PV (0.3, 0.1, 0.1)

=

B. Since PV of two year swap is zero, for remaining period exchange value PV = -0.107196

C. 18-24 month libor = a

(1+a/2)*(1+4%/2)*(1+4.4%/2)*(1+4.8%/2) = (1.045/2)^4

a = 4.8%

Exchange value 0.3 0.1 0.1 Discount rate 2% 2.10% 2.40% Discount factor 0.294118 0.095929 0.09368 PV 0.107196

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.