A. Determine the future periodic spot interest rates, at one period from now, on a one-step Ho-Lee model, using current periodic spot interest rate of A1 percent,current spot rate over two periods of A2 percent, and an annual interest rate volatilityof .005 (.5%). Then consider the current spot rate over three periods of A3 percent tofind the future periodic interest rates in a two-step Ho-Lee model. The period is A4months. Find the following

REST OF QUESTION ATTACHED (PDF)

USE UIN: 669116578 for BOND DATA (.xlsx)

Exam-3 for FIN415 Due by 12:30 p.m. on December 7, 2015 Read the following paragraph before proceeding You are required to submit in plain text, within the body of your email to sacharya@uic.edu, your UIN and then only two columns of numbers (with no special or alphabetical characters or formulas or explanation): (a) serial number of question and (b) your numerical answer. Write 999999 for all blank answers or undefined numbers. You are also required to attach to the email detailed works (scanned pdf or doc files and/or Excel sheets). You may additionally provide your answers in a separate Excel sheet, in addition to submitting the answers in plain text within your email. Non-numerical (alphabetical or special) characters or explanations for answers within the body of the email will not be accepted. Email submissions with works attached are due by the deadline. Answers submitted by any other means, after the deadline or without matching work will be treated as missing with zero credit. Each question carries equal weight. If you believe that more data are necessary to solve, assume whatever you think is necessary to answer the questions. All questions are required to be answered independently without any consultation with other students or professors. Take the data from the attached page corresponding to your UIN. Interest rates are expressed as annualized rates for the term specified. Report your interest rate answers as fractional numbers like 0.11 for 11% per year. A. Determine the future periodic spot interest rates, at one period from now, on a one-step Ho-Lee model, using current periodic spot interest rate of A1 percent, current spot rate over two periods of A2 percent, and an annual interest rate volatility of .005 (.5%). Then consider the current spot rate over three periods of A3 percent to find the future periodic interest rates in a two-step Ho-Lee model. The period is A4 months. Find the following. 1. 2. 3. 4. 5. 6. 7. 8. The trend (lambda1) in interest rate in the first period. The trend (lambda2) in interest rate in the second period. The future periodic rate on the upside at the end of one period. The future periodic rate on the downside at the end of one period. The future periodic rate at the up-most branch at the end of two periods. The future periodic rate at the middle branch at the end of two periods. The future periodic rate at the down-most branch at the end of two periods. The future periodic rate at the down-most branch at the end of two periods B. The cash futures price of a 3-month zero coupon bond with a face value of $100 for delivery in B1 months from now is B2 dollars. Suppose that the current spot Page 1 of 6 1 interest rate for a term of B3 months is B4 per cent per annum. Assume continuous compounding to answer the following: 9. The forward rate of interest for period B1 months to B1+3 months. 10. The spot rate of interest for period 0 to B1 months. 11. The current fair value of a B1-month zero coupon bond with $100 face. C. Consider C1-month spot interest rates evolving in the following two-step binomial tree over C2 months, i.e., with C1 months in each of the next two steps. The current C2-month spot interest rate is 5.15% and the C3-month spot interest rate is 5.3%. Find the following by assuming monthly compounding. 12. The risk neutral probability for the up move in first step. 13. The risk neutral probability for the up move in second step. 14. The current fair value of a C1-month European call option with a strike price of $974 written on a C2-month zero coupon bond with face value $1000. 15. The current fair value of a C2-month European put option with a strike price of $994 written on a C3-month zero coupon bond with face value $1000. 6.20% 5.30% 5.10% 4 50 5.10% 4.30% 4.00% D. Consider D1-month spot interest rates evolving in the following three-step binomial tree over D4 months, i.e., with D1 months in each of the next three steps. The current D3-month spot interest rate is 5.15%, the current D2-month spot interest rate is 5.3%, and the current D4-month spot interest rate is 5.45%. This three-step problem involves calculation of just the third step, because it is an extension of the two-step Problem C. Find the following by assuming monthly compounding. 16. The risk neutral probability for the up move in the last (third) step. Page 2 of 6 2 17. The current fair value of a D3-month European call option with a strike price of $974 written on a D4-month zero coupon bond with face value $1000. 18. The current fair value of a D2-month European put option with a strike price of $994 written on a D4-month zero coupon bond with face value $1000. 7.1% 6.2% 5.3% 5 5.1% 5 5.3% 5.1% 4.3% 4.3% 4.0% 3.7% E. Suppose that you are long in an original portfolio of 20-year bonds with a total face value of E1 million dollars and that you want to hedge the portfolio value against fluctuating interest rates by trading on a 10-year bond and a 30-year bond. You have estimated (given): DV0110 = E2, DV0120 = E3, and DV0130 = E4 per $100 face value of 10-year, 20-year and 30-year bonds, respectively. You have also used yield data on these bonds to estimate the coefficients, b=1.3 and c = 1.6, in the following regression: yt20 a byt10 cyt30 t . Using the given data, determine your optimal trading strategy for the 10-year and 30year bonds to hedge 20-year bonds. Report answers for the following: 19. Face value in dollars of 10 year bonds needed for hedging. 20. Face value in dollars of 30 year bonds needed for hedging. Page 3 of 6 3 After hedging, suppose that you observe that the 20-year yield moves by E5 basis points when the 10-year yield moves by 1 basis point and that the 20-year yield moves by E6 basis points when the 30-year yield moves 1 basis point. Then: 21. How much will be your profit or loss corresponding to 30-year yield increasing by 1 basis point? F. A collared floater is like a variable rate bond, but with an upper limit and a lower limit on the rate of coupon payment. Consider, for example, annual rates coupon payment and one-year spot interest rates. In the following table, the current one-year spot interest rate is denoted by r in column (1). Depending on the current spot interest rate, the collared floater with a face value of F1 dollars will pay the holder of this floater a sum a year later, as given in column (2) of the table. The binomial tree below gives the evolution of one-year spot interest rates over a four year period. 22. What is the current fair value of the four-year collared floater if the riskneutral probabilities in the binomial tree are 0.5 and 0.5 for the up and down moves, respectively? Current Rate, r (1) r 8% Collared Floater with face value F1 pays at the end of the year (2) F2 F1 x r% F3 10.50% 8.75% 6.2% 4.5% 9.50% 6.00% 5.2% 6.25% 5.50% 4.75% Page 4 of 6 4 G. A four-year participating cap pays an interest based on a nominal principal of G1, at the end of the year if the current annual spot interest rate, r, is higher than 5%. If the current annual spot rate, r, is less than 5%, the participating cap obligates its holder to lose 30% of (5%-r%) on the nominal principal at the end of the year. The payments are given in column (2) of the following table, given the rates in column (1). The binomial tree below gives the evolution of one-year spot interest rates over a four year period. 23. What is the current fair value of the participating cap if the risk-neutral probabilities in the binomial tree are 0.5 and 0.5 for up and down moves, respectively? Current rate, r (1) r > 5% r 5% Buyer gets at end of year (2) (r% - 5%)xG1 -.30(5% - r%)xG1 8.7% 6.8% 5.3% 4.0% 6.2% 4.8% 3.7% 4.3% 3.3% 3.1% H. What is the risk spread of a H1 percent annual coupon, 3.35 year maturity, and 100-face value bond? The bond pays the annual coupon in two equal installments and trades now at a quoted spot price of H2. Assume continuous compounding and Page 5 of 6 5 use the term structure of discount factors, d(t) = 1 - .03t - .0075t2 + .0015t3. Report answer for the following: 24. Risk Spread of the bond Page 6 of 6 6 654784434 A1 A2 A3 4.9 5.15 B1 B2 B3 6.9 97.55 C1 C2 C3 3 6 D1 D2 D3 3 6 E1 E2 E3 3.9 0.16 F1 F2 F3 190 9.5 G1 190 H1 H2 6.9 108.66 672477838 A1 A2 A3 5.8 6.05 B1 B2 B3 7.8 97.1 C1 C2 C3 4 8 D1 D2 D3 4 8 E1 E2 E3 4.8 0.17 F1 F2 F3 280 14 G1 280 H1 H2 7.8 109.79 658888740 A1 A2 A3 6.7 6.95 B1 B2 B3 8.7 96.65 C1 C2 C3 5 10 D1 D2 D3 5 10 E1 E2 E3 5.7 0.18 F1 F2 F3 370 18.5 G1 370 H1 H2 8.7 110.92 669116578 A1 A2 A3 7.6 7.85 B1 B2 B3 9.6 96.2 C1 C2 C3 6 12 D1 D2 D3 6 12 E1 E2 E3 6.6 0.19 F1 F2 F3 460 23 G1 460 H1 H2 9.6 112.05 664970417 A1 A2 A3 8.5 8.75 B1 B2 B3 10.5 95.75 C1 C2 C3 7 14 D1 D2 D3 7 14 E1 E2 E3 7.5 0.2 F1 F2 F3 550 27.5 G1 A4 5.25 2.9 B4 9.9 10.8 9 D4 9 E4 0.22 0.33 12 E5 E6 1.49 1.19 15.2 A4 6.15 3.8 B4 10.8 12.6 12 D4 12 E4 0.23 0.34 16 E5 E6 1.58 1.28 22.4 A4 7.05 4.7 B4 11.7 14.4 15 D4 15 E4 0.24 0.35 20 E5 E6 1.67 1.37 29.6 A4 7.95 5.6 B4 12.6 16.2 18 D4 18 E4 0.25 0.36 24 E5 E6 1.76 1.46 36.8 A4 8.85 6.5 B4 13.5 18 21 D4 21 E4 0.26 0.36 44 28 E5 E6 1.85 1.55 550 H1 H2 10.5 113.18 677851922 A1 A2 A3 9.4 9.65 B1 B2 B3 11.4 95.3 C1 C2 C3 8 16 D1 D2 D3 8 16 E1 E2 E3 8.4 0.2 F1 F2 F3 640 32 G1 640 H1 H2 11.4 114.31 A4 9.75 7.4 B4 14.4 19.8 24 D4 24 E4 0.26 0.37 32 E5 E6 1.94 1.64 51.2 652433262 A1 A2 A3 A4 10.3 10.55 10.65 8.3 B1 B2 B3 B4 12.3 94.85 15.3 21.6 C1 C2 C3 9 18 27 D1 D2 D3 D4 9 18 27 36 E1 E2 E3 E4 E5 E6 9.3 0.21 0.27 0.38 2.03 1.73 F1 F2 F3 730 36.5 58.4 G1 730 H1 H2 12.3 115.44 654896597 A1 A2 A3 A4 11.2 11.45 11.55 9.2 B1 B2 B3 B4 13.2 94.4 16.2 23.4 C1 C2 C3 10 20 30 D1 D2 D3 D4 10 20 30 40 E1 E2 E3 E4 E5 E6 10.2 0.22 0.28 0.39 2.12 1.82 F1 F2 F3 820 41 65.6 G1 820 H1 H2 13.2 116.57 659869110 A1 A2 A3 A4 12.1 12.35 12.45 10.1 B1 B2 B3 B4 14.1 93.95 17.1 25.2 C1 C2 C3 11 22 33 D1 D2 D3 D4 11 22 33 44 E1 E2 E3 E4 E5 E6 11.1 0.23 0.29 0.40 2.21 1.91 F1 F2 F3 910 45.5 72.8 G1 910 H1 H2 14.1 117.7 676769598 A1 A2 A3 A4 13 13.25 13.35 B1 B2 B3 B4 15 93.5 18 C1 C2 C3 12 24 36 D1 D2 D3 D4 12 24 36 E1 E2 E3 E4 12 0.24 0.3 0.41 11 27 48 E5 E6 2.30 2.00 F1 F2 1000 F3 50 G1 1000 H1 H2 15 118.83 80