Today is May 15, 2000.
(a) Compute (bootstrap) the discount curve Z(0, T) for T =6 month, 1 year, and 1.5 years from the following data:
• A 6-month zero coupon bond priced at $96.80 (issued 5/15/2000)
• A 1-year note with 5.75% coupon priced at $99.56 (issued 5/15/1998)
• A 1.5-year note with 7.5% coupon priced at $100.86 (issued 11/15/1991)
(b) Once you get the discount curve Z(0, T) you take another look at the data and you find the following 1-year bonds:
i. A 1-year note with 8.00% coupon (semi-annual) priced at $101.13 (issued 5/15/1991)
ii. A 1-year bond with 13.13% coupon (semi-annual) priced at $106.60 (issued 4/2/1981)
Compute the prices for these bonds with the discounts you found. Are the prices the same as what the market says? Is there an arbitrage opportunity? Why?