Problem 3. (14 points) Consider the following rate and price tree for a straight bond. 981.65 9% 991.20 VHH=? 7.5% 1,027.46 6% VL=? VH=? 1,009.43 6% 1,047.02 VHL=? 4.5% VL=? 1,038.83 3% VLL =? Find the missing prices for a European put option on the bond. The option expires at the end of the second year and has an exercise price of $1,020. Also, determine whether or not it would be optimal for the holder to exercise early at the end of the first year at node H?
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- H5. Which of the following is the name of the semiannual payment of $20 that you receive on a bond you own? a. Face Value b. Discount c. Yield d. Call Premium e. Coupon Explain with details and also explain wrong optionsQuestion 3. A fixed rate bond with notional 1 pays annual coupons of c at times T1, T2, . . . , Tn where Ti+1 = Ti + 1 and notional 1 at time Tn. a) Write down the bond price BFXD c (t) at time t ≤ T0 in terms of ZCBs. b) Suppose t = T0 = 0. The yield of the bond is defined as the value Y such that B FXD c (0) = Xn i=1 c (1 + Y ) i + 1 (1 + Y ) n , that is, the rate at which IRR discounting gives the bond price. By summing a geometric series, show that BFXD c (0) = 1 if and only if Y = c. c) By writing a swap as the difference between a fixed rate bond and a floating rate bond, show that BFXD c (0) = 1 if and only if c = y0[0, Tn]. Remark 1. This exercise shows that the T-year spot swap rate is the bond coupon such that a T-maturity bond has price par, that is 100% of notional.The following is a T-bond quote (par value $1,000) from the WSJ (8/31/2018). Use the information in the quote to answer the question. Maturity Coupon Bid Asked Chg Asked Yield 8/31/2,034 11.68 104:15 104:20 -14 ??? How much is the premium or discount of this bond? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16). Use a negative sign to represent a discount.)
- 13. Consider a coupon bond with coupon payment=4.25, M=100, and n=2. Suppose ?1 = 4% and ?2 = 4.24%. Consider a forward contract for the delivery of the coupon bond in one period from today. Calculate the forward price using the following two approaches: 1) use the forward rate to price the forward contract; 2) use the cost of carry approach: spot-forward parity adjusted for the coupons.If a P1,000 bond sells for P1,125, which of the following statements are correct? I. The market rate of interest is greater than the coupon rate on the bond. II. The coupon rate on the bond is greater than the market rate of interest. III. The coupon rate and the market rate are equal. IV. The bond sells at a premium. V. The bond sells at a discount. a. I and IV b. I and V c. II and IV d. II and VPlease answer the following question: The modified duration and convexity of a 6%, 25 year bond selling toyield 9% is 10.62 and 91.46 respectively. If the required yield increasesby 300 basis points from 9% to 12% what is the approximate percentagechange in the price of the bond due toa) duration,b) convexity,c) duration and convexity?d) If the actual change is -26.50%, compare your results from a) and c)which provides a better approximation?
- Consider a bond with a face value of $1000. An increase and decrease in 1 bp results in the price changing to 995.12707 and 996.09333, respectively. What is its PVBP?What is the price of the following bond? Face value/redemption price : P1,037 Maturity: 10yrs Coupon rate: 9% Discount rate: 9% **Coupon rate (regular payment) Pls show the whole solution thank you!Q30 If the price of the perpetual bond is OMR 375 with a coupon rate of 5%. What is the required rate of return of such bond (r), assume that the face of the bond is OMR 100? a. 1.33% b. 5.7% c. 7.5% d. 13.33%
- You are given the following prices and cash flows associated with bonds. CF stands for cash flow. Bond Price Today CF Year 1 CF Year 2 CF Year 3 A 105.185 10 10 110 B 90.371 100 0 0 C 91.784 5 105 0 D X 15 15 115 What is the current price of Bond D as per the no-arbitrage principle? In other words, what is the value of X?(PLEASE READ THIS DIRECTION)Rules for Bond Valuation Problem Solving:a. For the "PV FACTOR in computing the PV of the coupon and PV for the maturity value/ principal use until 8-9th decimal place" before multiplying the coupon payment or future value.Example: ___x 2.123456789 or 22.12345678b. For "COMPOUNDED RATES" include all decimals in the rate (do not round off).Example semi-annual: 13%/2 =0.065c. For the "VALUE OF THE BOND/ PRICE OF THE BOND" round off your answers and final answers into whole numbers.Example: 824.59= 825 3. Assume that Greenwich and Pizza Hut have similar P100,000 par value bond issues outstanding. The bonds are equally risky. Pizza Hut bond has an annual coupon rate of 8 percent and matures 20 years from today, the nominal annual rate of return is 12%. Greenwich's bond has a coupon rate of 8 percent, with interest paid semiannually, matures in 20 years, and nominal required rate of return 12 percent on a semi-annual basis. What is the DIFFERENCE in current…(PLEASE READ THIS DIRECTION)Rules for Bond Valuation Problem Solving:a. For the "PV FACTOR in computing the PV of the coupon and PV for the maturity value/ principal use until 8-9th decimal place" before multiplying the coupon payment or future value.Example: ___x 2.123456789 or 22.12345678b. For "COMPOUNDED RATES" include all decimals in the rate (do not round off).Example semi-annual: 13%/2 =0.065c. For the "VALUE OF THE BOND/ PRICE OF THE BOND" round off your answers and final answers into whole numbers.Example: 824.59= 825 1. A bond issued by Delta Corporation matures in 12 years. It has a 12.5 percent annual coupon rate and a face value of P10,000. The bond has a discount rate to maturity of 9.5 percent. What is the price of Omega's bond today?