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73323142-4-Int-rates - T ER Interest Rates Interest rates...

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TER Interest Rates Interest rates are a factor in the valuation of virtually all derivatives and will feature prominently in much of the material that will be presented in the rest of this book. In this chapter we cover some fundamental issues concerned with the way interest rates are measured and analyzed. We explain the compounding frequency used to define an interest rate and the meaning of continuously compounded interest rates, which are used extensively in the analysis of derivatives. We cover zero rates, par yields, and yield curves, discuss bond pricing, and outline a procedure commonly used by a derivatives trading desk to calculate zero-coupon Treasury interest rates. We cover forward rates and forward rate agreements and review different theories of the term structure of interest rates. Finally we explain the use of duration and convexity measures to determine the sensitivity of bond prices to interest rate changes. Chapter 6 will cover interest rate futures and show how the duration measure can be used when interest rate exposures are hedged. For ease of exposition we will ignore day count conventions throughout this chapter. The nature of these conventions and their impact on calculation~ will be discussed in Chapters 6 and 7. 4.1 TYPES OF RATES An interest rate in a particular situation defines the amount of money a borrower promises to pay the lender. For any given currency, many different types of interest rates are regularly quoted. These include mortgage rates, deposit rates, prime borrowing rates, and so on. The interest rate applicable in a situation depends on the credit risk. This is the risk that there will be a default by the borrower of funds, so that the interest and principal are not paid to the lender as promised. The higher the credit risk, the higher the interest rate that is promised by the borrower. Treasury Rates Treasury rates are the rates an investor earns on Treasury bills and Treasury bonds. These are the instruments used by a government to borrow in its own currency. Japanese Treasury rates are the rates at which the Japanese government borrows in yen; US Treasury rates are the rates at which the US government borrows in US dollars; and so 75
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76 CHAPTER 4 on. It is usually assumed that there is no chance that a government will default on an obligation denominated in its own currency.l Treasury rates are therefore totally risk-free rates in the sense that an investor who buys a Treasury bill or Treasury bond is certain that interest and principal payments will be made as promised. Treasury rates are important because they are used to price Treasury bonds and are sometimes used to define the payoff from a derivative. However, derivatives traders (particularly those active in the over-the-counter market) do not usually use Treasury rates as risk-free rates. Instead they use LIBOR rates.
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