A regional bank is restructuring part of its balance sheet and decides to issue a 3-year inverse floating-rate note (inverse floater). The coupon resets annually and is linked inversely to short-term interest rates, so investors benefit if rates fall. Analysts value the note using a 3-year binomial interest-rate lattice, calibrated from market par and forward rates.   Bond details Face Value: $100.00 Reset/Payment Frequency: Annual (coupon paid at each year-end) Coupon Formula: Coupon at time t=K−Lt\text{Coupon at time } t = K – L_tCoupon at time t=K−Lt​ where• K=[k]%K = [k]\% is the fixed base rate chosen by the issuer,• LtL_t is the 1-year short rate at the start of each period (from the lattice). Today’s 1-year spot rate: [z1]% 1-year forward rates starting 1 year from today (t=1):• Node B: [f11b]%• Node C: [f11c]% 1-year forward rates starting 2 years from today (t=2):• Node D: [f21d]%• Node E: [f21e]%• Node F: [f21f]% At maturity (t=3), the bond also pays back the principal $100. The fixed rate used to calculate coupons ( e.g., k minus f#,# ) is [k]%.    Task:Using the lattice, estimate the price today by backward induction under equal risk-neutral branch probabilities (0.5). Discount each node’s expected cash flow by the local 1-year short rate at that node.   Hint1: Given your experience at this point of this class, valuation of an inverse floater should be like riding a bike!  Step 1: Keep in mind the calibrated rates are already given to you. No need to calibrate the tree. Step 2: What is my coupon rate? In the case of inverse-floaters, it is simply the base rate (k) minus the interest rate shown on each node of the tree. Hence, you will have a different coupon on each node.  Step 3: Solve the tree backwards (starting from the terminal nodes), as usual.    Hint2: The higher the market (binomial tree) rates, the lower your inverse floater coupon will be. Theoretically, the coupon may be negative if any of the rates in the tree is higher than your base rate. In practice, this is usually avoided by setting a floor at zero (so the coupon cannot be lower than zero). 

Follow the guidelines listed below in order to open a blank Excel Spreadsheet. I wish you the best of luck! Once the spreadsheet opens, do not click on the refresh button. Doing so would erase your work. —- OPEN EXCEL SPREADSHEET: Click on the arrow next to either of the two files below. You may use this spreadsheet throughout the exam. Keep in mind the spreadsheet will NOT be saved when you submit your exam. Next, create a new sheet in the Respondus LockDown Browser spreadsheet. You can use this blank spreadsheet to calculate the answer. Make the column you are using as wide as possible. Otherwise, you might be seeing only the last decimals. Blank Spreadsheet-1.xlsx

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to be late

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