Today is June 7, 2007. Freddie Mac is issuing a 10-year Bermudan note on June 15 2007 under the terms described in Table 12.14¹⁰. A Bermudan security is like a callable security, but with call dates defined ex-ante in the term sheet. Prices of Treasury bills and notes for the same date are in Table 12.15.

(a) From the Treasury data obtain the discount curve Z(0, T) up to June 2017. Plot your results. (You can use bootstrap, or curve fitting, or any other methodology. See Chapter 2.)

(b) From the discount curve Z(0, T), fit a simple semi-annual BDT model, as in Chapter 11. Assume a constant &

Table 12.14 Freddie Mac, June 2017, 6% Fixed Rate Medium-Term Bermudan Note Issue Date Maturity Date Subject to Redemption Redemption Date(s) June 15, 2007 June 15, 2017 Yes. The Medium-Term Notes are redeemable at our [Freddie Mac) option, upon notice of not less than 5 Business Days, at a price of 100% of the principal amount, plus accrued interest to the Redemption Date Semi-annually, on June 15 and December 15, commencing on June 15, 2009. 6% Semiannually, in arrears, commencing December 15, 200 June 15 and December 15 at maturity, or upon redemption 3128X6CD6 Interest Rate Per Annum Frequency of Interest Payments Interest Payment Dates Principal Payment CUSIP Number Table 12.14 Freddie Mac, June 2017, 6% Fixed Rate Medium-Term Bermudan Note Issue Date Maturity Date Subject to Redemption Redemption Date(s) June 15, 2007 June 15, 2017 Yes. The Medium-Term Notes are redeemable at our [Freddie Mac) option, upon notice of not less than 5 Business Days, at a price of 100% of the principal amount, plus accrued interest to the Redemption Date Semi-annually, on June 15 and December 15, commencing on June 15, 2009. 6% Semiannually, in arrears, commencing December 15, 200 June 15 and December 15 at maturity, or upon redemption 3128X6CD6 Interest Rate Per Annum Frequency of Interest Payments Interest Payment Dates Principal Payment CUSIP Number