Topic 11B - Accrued interest, clean and dirty prices, yield curve models, and forward rates. After completing this unit, you should be able to: Compute bond accrued interest and invoice price, construct yield curves using an empirical curve fitting and theoretical model, compute forward interest rates given zero-coupon spot interest rates. | Financial Modeling Topic #11b: Accrued Interest, Clean and Dirty Prices, Yield Curve Models, and Forward Rates L. Gattis 1 Learning Objectives Compute bond accrued interest and invoice price Construct yield curves using an empirical curve fitting and theoretical model Compute forward interest rates given zero-coupon spot interest rates 2 Clean and Dirty Prices When you buy a bond between coupon payment dates, you must pay the seller the quoted price (, clean price) plus accrued interest Accrued Interest: Coupon Payment x Accrual Factor Accrual Factor = Days since last pmt / Total days between pmts Dirty “Invoice” Price (Paid to Bond Seller) Quoted price plus accrued interest Present Value of all future coupon payments and par .: $100 Par, 10% Annual Coupon Bond immediately prior to maturity PV = $110, Quoted Price = $100, Dirty (Invoice) due seller is $110 Clean Price = Dirty Price - Accrued Interest Clean price is also the Quoted price Excel’s price function compute the Clean Price Clean (Quoted) prices are less volatile because it not go up and down with coupon payments 3 Excel’s “Clean” and “Dirty” Prices 4 4 Bloomberg IBM Bond DES 5 30/360 Day Count Convention 360: Assume 360 Days/Year, 180 Days between coupon pmt dates 30: Assume 30 days per month in counting days since last coupon Excel’s Days360(date1, date2) function returns the number of days between two dates assuming 30/month Accrual Method: IBM 6 IBM Bond YIELD and MDURATION 7 Term Structure The Term Structure of Interest Rates shows securities yields (of similar credit risk) across maturities 8 Polynomial Curve Fitting (Yahoo Finance Data) 9 Select Maturity and YTM, Insert xy scatter (markers only), right click on series, add trend line – 3rd order Polynomial Polynomial Curve Fitting (Yahoo Finance Data) 10 Select last 2 columns, Insert xy scatter, right click on series, add trend line – 3rd order Polynomial Polynomial Curve Fitting (Yahoo Finance Data) 11 Regression Results – Use regression . | Financial Modeling Topic #11b: Accrued Interest, Clean and Dirty Prices, Yield Curve Models, and Forward Rates L. Gattis 1 Learning Objectives Compute bond accrued interest and invoice price Construct yield curves using an empirical curve fitting and theoretical model Compute forward interest rates given zero-coupon spot interest rates 2 Clean and Dirty Prices When you buy a bond between coupon payment dates, you must pay the seller the quoted price (, clean price) plus accrued interest Accrued Interest: Coupon Payment x Accrual Factor Accrual Factor = Days since last pmt / Total days between pmts Dirty “Invoice” Price (Paid to Bond Seller) Quoted price plus accrued interest Present Value of all future coupon payments and par .: $100 Par, 10% Annual Coupon Bond immediately prior to maturity PV = $110, Quoted Price = $100, Dirty (Invoice) due seller is $110 Clean Price = Dirty Price - Accrued Interest Clean price is also the Quoted price Excel’s price function compute the Clean
