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- Suppose that x is the continuously compounded yield to maturity on a zero-coupon bond that pays off $1 at time T. Assume that x follows the process: dx = a (x₁ - x) dt + sx dz where a, x0, and s are positive constants and dz is a Wiener process. What is the process followed by the bond price? Solutions:Consider a 1-factor parallel yield shift model with a flat structure of interest rates and consider two bonds with the same maturity time T but with different coupon rates. Which bond has a higher duration? A) The bond with a lower coupon rate B) The bond with a higher coupon rate C) The Durations of these two bonds are the sameExplain what you see from the pricing calculations. How do the two bonds differ? Bond C Bond Price = PV(rate,nper,pmt,fv) Given: n = Period which takes values from 0 to the nth period = 0,1,2,3 & 4 Cn = Coupon payment in the nth period = 10%*$1,000 = $100 YTM = interest rate or required yield = 9.6% P = Par Value of the bond = $1,000 Bond Z Bond Price = PV(rate,nper,pmt,fv) Given: n = Period which takes values from 0 to the nth period = 0,1,2,3 & 4 Cn = Coupon payment in the nth period = 0%*$1,000 = $0.00 YTM = interest rate or required yield = 9.6% P = Par Value of the bond = $1,000 years Bond A Bond Z 4 $1,012.79 $693.04 3 $1,010.02 $759.57 2 $1,006.98 $832.49 1 $1,003.65 $912.41 0 $1,000.00 $1,000.00
- A fixed rate bond with notional 1 pays annual coupons of c at times T1,T2,...,Tn whereTi+1 =Ti+1andnotional1attimeTn. a) Write down the bond price Bc^(FXD)(t) at time t ≤ T in terms of ZCBs.For a discount bond, the current yield isthe yield to maturity, and the coupon rate is the yield to maturity. Select one: O a. less than; less than O b. equal to; equal to O c less than; greater than O d. greater than; greater than O e. greater than; less thanWhich of the following statements is/are most CORRECT? O 11 A yield curve depicts the relationship between bond's 'time to maturity and its yield to maturity. 2) A premium bond's price will decline over time if the required return remains unchanged. 3) A discount bond's price will decline over time if the required return remains unchanged. 4) Both a and b are correct.
- Can the price of bond B be determined using the PV function or any other function in excel? What is the EAR (effective annual rate) of these two bonds?If the yield of maturity of the bond is equal the coupon rate, the price of this bond will be? a. Lower than the par value. b. Equal the par value. c. Higher than the par value.The yield to maturity on a bond with a price equal to its par value will Select one: a. Will depend upon the required return. b. Will be lower than the coupon rate. c. Always be equal to the coupon rate. d. Will be more than the coupon rate
- A bond’s expected return is sometimes estimated by its yield to maturity (YTM) and sometimes by its yield to call (YTC). The YTC is a better estimate when the bond sells at... a. a discount. b. a premium. c. par value.The yield to maturity on a bond a is fixed in the indenture. b is lower for higher-risk bonds. c is the required return on the bond. d is generally equal to the coupon interest rate.The forward rate f(t1,12) of a bond, is the implicit interest rate in a future period between time t1 and t2. For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-r t1), and from period 0 to 12 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) exp(-r t2)). Suppose we observe the prices of a 14-year zero-coupon bond (with a face value of $93.31), where P(t1,t2) regans the price of the bond between t1 and 12, and a year 7-to-14 forward rate as follows:P(0.14) - $86.5496905000 and f(7,14) - 0.6074704253 %. Calculate the price of a 7-year zero-coupon, with face value $99.27: $82.9604 $96.0778 ✓(25 %) $96.2349 $82.1804