1. Yield To Maturity Formula

2. Yield to Maturity Equation - Closed Form (started with a geometric series…)
Calculate price of bond with par value of $1,000 to be paid in 10 years, a coupon of 10% and YTM of 12%.
Assume coupons are paid semi-annually to bond holders:
Determine number of coupon payments (2 per year for 10 years = 20)
Determine value of each coupon payment (divide coupon in half since semi-annual). Each payment will be $50 ($1000 * 0.05).
Determine the semi-annual yield: Like the coupon rate, the YTM of 12% must be divided by 2.

3. YTM - Frequency Parameterized
Accounting for different payment frequencies:
Most bonds pay semi-annually but to make our formula more general we extend formula with parameter “F” below.
if a bond was paying annual coupons F = 1, quarterly = 4

4. While more programmer friendly, what do we assume away with this formula?
Assumes all intermediate flows are discounted at same rate (the YTM)
A more general implementation is the “cash-flow series”
A collection of individual cash-flows which can:
Support assigning different interest rates to individual cash-flows
Represent changing principal amounts (e.g., for amortizing instruments)
Support independent processing of individual cash-flows (e.g., date adjustments)

5. Deliverables for next week:
Download the “living spec” prototype spreadsheet.
Build calculator class around PV function
Implement the closed form equation
Calculate price from yield and price sensitivity to yield change (first partial derivative) : “DV01” (dollar value of 1/100 of a percent)
Download sample code to load bond data file
File access utility class in “SBB_util.*”
Run your main() loading data.txt and call your executable from run.sh
You will need to calculate number of periods… (download the SBB_date.* code)
Output 3 rows of results 2 values per row to stdout:
“Price” “dv01” in each row separated by a space
Example: (in each row)