Six-month LIBOR is 5 %. LIBOR forward rates for the 6- to 12...

Six-month LIBOR is $5 \%$. LIBOR forward rates for the 6- to 12 -month period and for the 12- to 18 -month period are $5.5 \%$. Swap rates for 2- and 3-year semiannual pay swaps are $5.4 \%$ and $5.6 \%$, respectively. Estimate the LIBOR forward rates for for 18 months to 2 years, 2 to 2.5 years, and 2.5 to 3 years. Assume that the 2.5 -year swap rate is the average of the 2- and 3-year swap rates and that OIS zero rates for all maturities are $4.5 \%$. OIS rates are expressed with continuous compounding; all other rates are expressed with semiannual compounding.

Key Concepts

LIBOR

The London Interbank Offered Rate (LIBOR) is a benchmark interest rate at which major global banks lend to one another. It plays a crucial role in short-term interest rate markets and is used extensively as a base rate for various financial products, including derivatives, loans, and mortgages.

Forward Rates

Forward rates represent the future interest rates implied by current interest rate instruments. They are used to price financial derivatives and to infer market expectations of future short-term rates. Understanding forward rates is essential for determining the cost of borrowing or investing over future time periods.

Swap Rates

Swap rates are the fixed rates exchanged for floating rates in an interest rate swap, a derivative instrument frequently used for hedging or managing exposure to interest rate fluctuations. They provide market consensus on long-term interest rates and serve as important benchmarks across different maturities.

Compounding Conventions

Compounding conventions, such as semiannual or continuous compounding, determine how interest accrues over time. Semiannual compounding calculates interest twice a year, while continuous compounding assumes interest accumulates continuously, affecting the conversion between different interest rate measures and influencing the pricing and discounting of cash flows.

Zero Rates and Discount Factors

Zero rates, or spot rates, are the yields on zero-coupon bonds which pay no interim interest and are used to construct discount factors for different maturities. These discount factors are essential in present value calculations and in deriving forward rates and swap rates from market data.

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