Derivatives

CHAPTER 8Interest Rates

Aims

• To examine different conventions when returns or interest rates (yields) are ‘annualised’ – namely ‘simple interest’, ‘compound interest’ and ‘continuously compounded interest’.
• To calculate present value and terminal value using different interest rate conventions.
• Show how to switch between simple interest rates, compound rates and continuously compounded rates.
• To calculate forward rates from spot rates, using different interest rate conventions.
• To show how a Forward Rate Agreement (FRA) is priced.

This chapter provides an overview of the key interest rates used in the market and different day-count and interest rate conventions used when calculating ‘annual yields’. We also discuss how forward rates are derived from spot interest rates and how FRAs are priced.

8.1 LIBOR, REPOS, FED FUNDS, AND OIS RATES

8.1.1 LIBOR

LIBOR (London Interbank Offer Rate) is the interest rate at which an AA-rated bank agrees to lend out funds to another AA-rated bank. LIBOR is an unsecured loan and borrowing is for maturities of one day to one year. The rate quoted will often be an average of LIBOR rates taken from a survey of ‘reference banks’, usually at 11 a.m. London time, under the auspices of the British Bankers Association (BBA). This is known as the ‘LIBOR-fixing’ and provides a reference rate for use in valuing many derivatives transactions (e.g. interest rate swaps). In recent years there has been an investigation into manipulation of LIBOR rates submitted ...