1. A. Caggia, M.Armanini Financial Investments & Pricing 2015-2016
Pricing Bonds
A. Caggia, M.Armanini
Financial Investments & Pricing

6. Fixed Income Securities
Fixed income securities provide a certain Yield to Maturity (YTM), Note that the yield is certain only if the security is kept untill maturity!
Short Term Treasury (Treasury bills);
Government bonds;
Corporate bonds

7. Different Issuers of Bonds
U.S. Treasury
Notes and Bonds
Corporations
Municipalities
International Governments and Corporations
Innovative Bonds
Indexed Bonds
Structured (Floaters, Reverse Floaters)

8. Fixed Income Securities
Zero coupon bond: the only cash flow is the repyment in full at maturity;
Straight coupon bond:payment of annual or semiannual fixed coupons plus principal repayment at expiration;
Step up /step down bond: the coupon may change overtime; …

9. Zero coupon bond
The Bond is priced today price P and repaid at Z after a set period of time.
The simple capitalisation convention is used for period of times shorter than 1 year. Over 1 year the yearly capitalisation convention is used.
Time convention:
Actual/Actual
Actual/360
Actual/365
30/360

10. Straight coupon bond
A bond that pays a coupon on a regular basis (eg BTP).
Yield to Maturity (YTM) is generally used to calculate the yield of the coupon bond and it is equal to the interest rate that equals the Present value of the coupons and principal to today price.
A coupon bond price could be :
Corso tel quel (Dirty Price), including the prorata part of the present coupon (used for settlement)
Corso secco (Clean Price)

11. Bond Pricing PB = Price of the bond Ci = interest or coupon payments
n = number of periods to maturity
r = discount rate per period

12. Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000
PB = $1,148.77
Ct = 80 pa (40 SA)
P = 1000
T = 20 periods (10Y)
r = 3% semiannual

13. Yield to Maturity
Interest rate that makes the present value of the bond’s payments equal to its price
Solve the bond formula for r

14. YIELD TO MATURITY YTM Where: C = six months coupon
YTM = YTM for the period

15. Bond Prices and Yields
Prices and Yields (required rates of return) have an inverse relationship
When yields get very high the value of the bond will be very low
When yields approach zero, the value of the bond approaches the sum of the cash flows

16. Prices and Coupon Rates
Yield

17. Listing Where: C = Six Months Coupon n = years to maturity
r =six months rate
days= days between now and the coupon payment date