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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- Explain 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 $1,000.00The following graph is most likely CURVE CHART Display Range: 1M - 30Y Yield USBMK=4.525 5.6 5.4 5.2 5.0 4.8 4.6 4.4 1M 6M 1Y 3Y 5Y 7Y 10Y 20Y 30Y US Treasuries spot curve US Treasuries yield curve US Bond Market chart curveConsider a bond with a face value of $1000. An increase and decrease in 1 bp results in the price changing to 995.12707 and 996.09333, respectively. What is its PVBP?
- Question 3. A fixed rate bond with notional 1 pays annual coupons of c at times T1, T2, . . . , Tn where Ti+1 = Ti + 1 and notional 1 at time Tn. a) Write down the bond price BFXD c (t) at time t ≤ T0 in terms of ZCBs. b) Suppose t = T0 = 0. The yield of the bond is defined as the value Y such that B FXD c (0) = Xn i=1 c (1 + Y ) i + 1 (1 + Y ) n , that is, the rate at which IRR discounting gives the bond price. By summing a geometric series, show that BFXD c (0) = 1 if and only if Y = c. c) By writing a swap as the difference between a fixed rate bond and a floating rate bond, show that BFXD c (0) = 1 if and only if c = y0[0, Tn]. Remark 1. This exercise shows that the T-year spot swap rate is the bond coupon such that a T-maturity bond has price par, that is 100% of notional.4- Calculate the equilibrium interest rate of a 1-year discount bond with a face value of 1000. The demand and supply curves for this bond are represented by the following equations: ( B4: Price = -0.8 * Quantity + 1160 B": Price = Quantity +720Which bond should an investor choose: Dollar-denominated bond Euro-denominated bond i$ = 6% i€ = 8% spot exchange rate = .90 euro/$1 expected future spot exchange rate = .96 euro/$1 Assume a 1-year time horizon. Show all calculations. Also, explain in words.
- A convertible bond has a conversion ratio of 26.1. What is the conversion price? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16).) A. 36.65 B 38.31 C. 37.78 D. 36.41 E. 37.56Consider the following money market information being quoted: Which of the following statements is true? Particulars GBP Interest Rate THB Interest Rate Spot Rate 1-year Expected Spot Rate Bid Rate 6.100% 10.550% THB5.6601/GBP THB5.9037/GBP C. Ask Rate 6.125% 10.625% THB5.6622/GBP THB5.9961/GBP a. There is an arbitrage which can only be made by initially borrowing GBP and then investing in THB. b. More than one of the options in this question are correct. The THB is selling at a premium to the GBP in the future. O d. There is an arbitrage which can only be made by initially borrowing THB and then investing in GBP.Comment on the attractiveness of the bonds in two ways: a) How does the yield compare to the benchmark? Market YTM: 3.62% YTM of bond: 3.72% b) How does the current price compare to the benchmark-yield implied price? Price: 100.875 Implied price: 100.923
- Suppose that y is the yield on a perpetual government bond that pays interest at the rate of $1 per annum. Assume that y is expressed with simply com- pounding, that interest is paid annually on the bond, and that y follows the process dy = a(y0 −y)dt + oydWt, where a, y0, and o are positive constants and dWt is a Wiener process. (a) What is the process followed by the bond price? (b) What is the expected instantaneous return (including interest and capital gains) to the holder of the bond?This first table describes prevailing market interest rates. Market Data Yield 0.05 Required: Using the yield above and the information contained in the table below, please calculate the price and duration of the bond as well as all necessary steps. (Use cells A5 to B5 from the given information to complete this question.) Time Until Payment Payment Discounted Payment Weight Time × Weight 1.00 $30.00 2.00 $30.00 3.00 $30.00 4.00 $1,030.00 Price: Duration13. 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.