chapter 7 - FINA0301 Derivatives Faculty of Business and...

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Unformatted text preview: FINA0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Tao LIN Chapter 7 Interest Rate Forwards and Futures 1 Chapter Outline Basic bond concepts – coupon bonds, yields to maturity, and implied forward rates Interest rate forward and forward rate agreements, Eurodollar futures, interest rate strips and stacks Sensitivity of bond price to interest rate risk: duration and convexity Section 7.4 and 7.5 will not be covered or tested!! 2 Bond Basics U.S. Treasury Securities Bills (<1 year): no coupons, sell at discount Notes (1 – 10 years), Bonds (10 – 30 years): coupons, sell at a price close to par STRIPS : claim to a single coupon or principal portion of government bond. Trade separately from the bond. Can be considered as a zero-coupon bond itself. 3 Bond Basics (cont’d) Notation r t (t 1 ,t 2 ): interest rate from time t 1 to t 2 prevailing at time t P t 0 (t 1 ,t 2 ): price of a bond quoted at t = t to be purchased at t 1 maturing at t 2 When t = t 1 , the subscript can be dropped. Zero Coupon Yield to maturity: percentage increase in dollars earned from the zero coupon bond (Internal Rate of Return). YTM is different from coupon rate. 4 Bond Basics (cont’d) Zero-coupon bonds make a single payment at maturity 5 Bond Basics (cont’d) r (0,t): annual effective return One year zero-coupon bond: P(0,1) = 0.943396 Pay $0.943396 today to receive $1 at t=1 Yield to maturity (YTM) = 1/0.943396 – 1 = 0.06 r (0,1) = 6% Two year zero-coupon bond: P(0,2) = 0.881659 YTM = 1/0.881659 – 1 = 0.134225 = (1 + r (0,2)) 2 – 1 r (0,2) = 0.065 = 6.5% 6 Bond Basics (cont’d) Zero-coupon bond price that pays Ct at t: Zero Coupon Yield curve : graph of annualized zero coupon bond yields against time Implied forward rates Suppose current one-year rate r (0,1) and two-year rate r (0,2) Current forward rate from year 1 to year 2, r (1,2), must satisfy 7 P t C r t t t ( , ) [ ( , )] 1 [1 r (0,1)][1 r (1,2)] [1 r (0,2)] 2 Bond Basics: Implied Forward Rates 8 Figure 7.1 An investor investing for 2 years has a choice of (1) buying a 2-year zero-coupon bond paying [1+ r (0, 2)] 2 or (2) buying a 1-year bond paying 1+ r (0, 1) for 1 year, and reinvesting the proceeds at the implied forward rate, r (1, 2) between years 1 and 2. The implied forward rate makes the investor indifferent between these alternatives. Bond Basics: Implied Forward Rates In general: Example 7.1: What are the implied forward rate r (2,3) and forward zero- coupon bond price P (2,3) from year 2 to year 3? (use Table 7.1) 9 [ ( , )] [ ( , )] [ ( , )] ( , ) ( , ) 1 1 1 1 2 2 1 1 2 2 1 2 1 r t t r t r t P t P t t t t t r P P 2 3 0 2 0 3 1 0881659 0816298 1 0 0800705 ( , ) ( , ) ( , ) ....
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chapter 7 - FINA0301 Derivatives Faculty of Business and...

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