Please show as much work as possible, it was advised to use excel.

FIN 612 Fall 2015 Final Exam 1. A 4-year 12% coupon bond has a yield of 10%. a) What are its Macaulay Duration, Modified duration, and convexity (I do not mean effective convexity)? b) What is the actual price change, Modified Duration predicted price change and Modified Duration + convexity predicted change in price for an increase of 50 basis point in the yield. Assume a flat term structure before and after the increase and annual coupons. (Note: For convexity do not use effective convexity measure) 2. Consider the following bonds currently traded in the market. Using this information find the no-arbitrage price of a 5Year bond with a coupon of 5%. Suppose this bond is currently selling for $102 in the market. Is there an arbitrage opportunity? Show how you would execute this arbitrage i.e. the write down the steps, the cash flows at each period and show the arbitrage profit resulting from the cash flows? (All coupons are annual payment, including the bond you are asked to price) Annual Maturity Price Coupon in Years Bond 1 8% 1 102.800 Bond 2 9% 2 107.250 Bond 3 11% 3 116.400 Bond 4 6% 4 104.410 Bond 5 5 7% 108.030 Bond 6 6 8% 113.950 Bond 7 7 10% 127.020 3. Consider two portfolios A and B. The details are as follows Portfolio A: Six 12% coupon 2-Year Bonds, eight 3-Year 6% coupon Bonds Portfolio B: Five 10% coupon 1-Year Bonds, seven 3-Year 9% coupon Bonds. The current term structure is as follows 1-Year: 5%, 2-Year: 5.35%, 3-Year: 5.85%, 4-Year: 5.95%, What are the key rate Durations for the one, two and three years of each portfolio, their effective durations and what are the changes in value for a 50bps increase in the 1-year rate, 50 bps decrease in the two year rate and a 25 bps increase in the 3-Year rate. Assume annual coupons 4. Consider the following tree 0.338464 0.262012 0.196941 0.14318 0.1 0.245776 0.186493 0.137401 0.097916 0.17847 0.13274 0.095862 0.129596 0.09448 0.094106 a) What is the price of a 4-Year 9% coupon $100 Par bond that is callable at the end of Year 1 for $85 and from the end of Year 2 for $ 87, but is not callable in Year 3. b) What is the price of the embedded option? 5. 10.23 9.56 8.91 8.83 a) Use the adjacent interest rate tree to price an 8% coupon 4-Year $100 Par bond. The bond is puttable at the end of Year 1 for a price of $99.75, at the end of Year 2 for $99.85, and at the end of Year 3 at Par. 7.21 7.8 7.1 7.41 6.97 b) What is the option value? 6.35 6. 7.76 a) Use the adjacent tree to price a 4-year multi-step up callable bond. The bond pays a coupon of 4.5% for Year 1, 5.5% for Year 2 and 6.5% for Year 3. The bond is callable at $99 from Year 1 onwards. 6.21 b) What is the value of the option 9.32 7.01 5.43 5.74 3.45 4.45 4.7 5.03