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Options, Futures, and Other Derivatives

John C. Hull

Chapter 34

Swaps Revisited - all with Video Answers

Educators

Chapter Questions

Problem 1

Calculate all the fixed cash flows and their exact timing for the swap in Business Snapshot 34.1. Assume that the day count conventions are applied using target payment dates rather than actual payment dates.

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Problem 2

Suppose that a swap specifies that a fixed rate is exchanged for twice the LIBOR rate. Can the swap be valued using the "assume forward rates are realized" rule?

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02:34

Problem 3

What is the value of a 2-year fixed-for-floating compounding swap where the principal is $$\$ 100$$ million and payments are made semiannually? Fixed interest is received and floating is paid. The fixed rate is $8 \%$ and it is compounded at $8.3 \%$ (both semiannually compounded). The floating rate is LIBOR plus 10 basis points and it is compounded at LIBOR plus 20 basis points. The LIBOR zero curve is flat at $8 \%$ with semiannual compounding. The risk-free discount rate is $7.5 \%$ continuously compounded.

Breanna Ollech
Breanna Ollech
Numerade Educator
02:34

Problem 4

What is the value of a 5-year swap where LIBOR is paid in the usual way and in return LIBOR compounded at LIBOR is received on the other side? The principal on both sides is $$\$ 100$$ million. Payment dates on the pay side and compounding dates on the receive side are every 6 months. The LIBOR zero curve is flat at $5 \%$ with semiannual compounding and is used for discounting.

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 5

Calculate the total convexity/timing adjustment in Example 34.3 of Section 34.4 if all cap volatilities are $18 \%$ instead of $20 \%$ and volatilities for all options on 5 -year swaps are $13 \%$ instead of $15 \%$. What should the 5 -year swap rate in 3 years' time be assumed for the purpose of valuing the swap? What is the value of the swap?

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Problem 6

Explain why a plain vanilla interest rate swap and the compounding swap in Section 34.2 can be valued using the "assume forward rates are realized" rule, but a LIBOR-inarrears swap in Section 34.4 cannot.

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04:01

Problem 7

In the accrual swap discussed in the text, the fixed side accrues only when the floating reference rate lies below a certain level. Discuss how the analysis can be extended to cope with a situation where the fixed side accrues only when the floating reference rate is above one level and below another.

Alexander Allen
Alexander Allen
Numerade Educator

Problem 8

LIBOR zero rates are flat at $5 \%$ in the United States and flat at $10 \%$ in Australia (both annually compounded). In a 4-year diff swap Australian LIBOR is received and $9 \%$is paid with both being applied to a USD principal of $$\$ 10$$ million. Payments are exchanged annually. The volatility of all 1-year forward rates in Australia is estimated to be $25 \%$, the volatility of the forward USD/AUD exchange rate (AUD per USD) is $15 \%$ for all maturities, and the correlation between the two is 0.3 . What is the value of the swap? Assume a USD discount rate of $4.7 \%$ continuously compounded.

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Problem 9

Estimate the interest rate paid by $P\&G$ on the $5 / 30$ swap in Section 34.7 if (a) the CP rate is $6.5 \%$ and the Treasury yield curve is flat at $6 \%$ and (b) the CP rate is $7.5 \%$ and the Treasury yield curve is flat at $7 \%$ with semiannual compounding.

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Problem 10

Suppose that you are trading a LIBOR-in-arrears swap with an unsophisticated counterparty who does not make convexity adjustments. To take advantage of the situation, should you be paying fixed or receiving fixed? How should you try to structure the swap as far as its life and payment frequencies?

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02:34

Problem 11

Suppose that all 12 -month LIBOR forward rates are $5 \%$ with annual compounding. The OIS zero curve is flat at $4.8 \%$ with continuous compounding. In a 5 -year swap, company X pays a fixed rate of $6 \%$ and receives LIBOR. The volatility of the 2 -year swap rate in 3 years is $20 \%$.
(a) What is the value of the swap?
(b) Use DerivaGem to calculate the value of the swap if company $\mathrm{X}$ has the option to cancel after 3 years.
(c) Use DerivaGem to calculate the value of the swap if the counterparty has the option to cancel after 3 years.
(d) What is the value of the swap if either side can cancel at the end of 3 years?

Breanna Ollech
Breanna Ollech
Numerade Educator
01:22

Problem 12

How would you calculate the initial value of the equity swap in Business Snapshot 34.3 if OIS discounting were used?

Jennifer Stoner
Jennifer Stoner
Numerade Educator