5) Let the six-month interest rate be 8%. To satisfy no-arbitrage, assume the six month rate moves up or down by 25 bp each six-month period with equal probability. Build an interest rate tree and value a two-year, 8.2% callable bond that can be called for par ($100). What is the value of the embedded option?
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- What would be the value of the bond described in Part d if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13% return? Would we now have a discount or a premium bond? What would happen to the bond’s value if inflation fell and rd declined to 7%? Would we now have a premium or a discount bond? What would happen to the value of the 10-year bond over time if the required rate of return remained at 13%? If it remained at 7%? (Hint: With a financial calculator, enter PMT, I/YR, FV, and N, and then change N to see what happens to the PV as the bond approaches maturity.)Bond B is a 2-year maturity coupon-paying bond with annual coupon of 10 and face value of 110. The yield curve is flat at 4% per year. Consider a forward contract F on one bond B. If the forward F's maturity is 15 months from now, what is the no-arbitrage forward price F0, 15 months? Enter your answer with 2 decimal places after the point.You find a zero coupon bond with a par value of $10,000 and 19 years to maturity. If the yield to maturity on this bond is 5.7 percent, what is the dollar price of the bond? Assume semiannual compounding periods
- Suppose a five-year face value of $1000 bond with a 9% coupon rate, and coupons are paid semi-annually. The yield to maturity of this bond is 7% (APR with semi-annual compounding). a) Is this bond trading at a discount, at par, or a premium? Explain. b) If the bond's yield to maturity rises to 8% (APR with semi-annual compounding), what price will the bond trade for?You can enter into a forward contract for a bond with a maturity in one year months that pays a coupon payment of $25 every six months. The bond has a forward price of $930. The current zero coupon rate for 6 months is 4% annually and the zero coupon risk free rate for one year is 5% annually (assume continuous compounding). The current price of the bond is $943. Use the equilibrium forward price equation (F=Sert) adjusted for both coupon payments to see if an arbitrage opportunity exists. If arbitrage is possible, explain the arbitrage opportunity that exists and show how the profit can be earned – make sure to explain every step in detail in realizing the profit and establishing the arbitrage. If arbitrage is not possible, show how you know it is not possible. ANSWER IN TYPING OTHER WISE DOWNVOTE YOUThe 3-year, 5-year, and 7-year zero rates are 1%, 2%, and 3%. The rates are given per annum with annual compounding. a) What are the zero-coupon bond prices with maturities of 3 years, 5 years, and 7 years? (Assume that you receive a face value of $100 for each of these bonds on their maturity dates). b) What is the forward rate for an investment initiated 3 years from today and maturing 5 years from today? (Give your answer per annum with continuous compounding)? c) What is the forward rate for an investment initiated 3 years from today and maturing 7 years from today? (Give your answer per annum with annual compounding)?
- Suppose that a 12-year bond pays semiannual coupons that increase by 4 dollars with each coupon. If the first coupon is for 30 dollars, the yield rate is 7.6 percent convertible semiannually, and the redemption value is 2000 dollars, find the price of the bond. Answer =You find a zero coupon bond with a par value of $20,000 and 16 years to maturity. If the yield to maturity on this bond is 5.4 percent, what is the dollar price of the bond? Assume semiannual compounding periods. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)Suppose that we expect $1 million in 3 months and that we want to invest it for a period of 6 months. We also want to set today the rate at which we can invest this money. It is possible to recreate the same result as a forward rate agreement by taking a long position in a 3-month zero-coupon bond and a short position in a 9-month zero-coupon bond True Faux
- Suppose that a bond has a face value of $200 000 and its maturity date is 10 years from now. The coupon rate is 5% payable semi-annually. Find the fair price of this bond, assuming that the annual market rate is 4%.A firm is going to issue a 15-year bond with semi-annual coupon payments. The face value is $1,000 and the coupon rate is 6% per year. If the market requires an annual return of 5% on the bond, the bond price should be ________. Question 20 options: A) $1,105 B) $884 C) $1,037 D) $926A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 9%, and sells for $1,100. Interest is paid annually. Assume a face value of $1,000 and annual coupon payments.a) If the bond has a yield to maturity of 9% 1 year from now, what will its price be at that time?b) What will be the rate of return on the bond? c) If the inflation rate during the year is 3%, what is the real rate of return on the bond? Assume annual interest payments.