1 / 23

Pricing of Bonds

Pricing of Bonds. Zvi Wiener Based on Chapter 2 in Fabozzi Bond Markets, Analysis and Strategies. Time value of money How to calculate price of a bond Why the price of a bond changes Relation between yield and price Relation between coupon and price Price changes when approaching maturity

ady
Download Presentation

Pricing of Bonds

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pricing of Bonds Zvi Wiener Based on Chapter 2 in Fabozzi Bond Markets, Analysis and Strategies http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  2. Time value of money • How to calculate price of a bond • Why the price of a bond changes • Relation between yield and price • Relation between coupon and price • Price changes when approaching maturity • Floaters and inverse floaters • Accrued interest and price quotes Fabozzi Ch 2

  3. -PV 5 5 5 5 105 Time Value of Money • present value PV = CFt/(1+r)t • Future value FV = CFt(1+r)t • Net present value NPV = sum of all PV Fabozzi Ch 2

  4. Time Value • You have $100 now and are going to deposit it for 5 years with 6% interest. • What will be the final amount? • It depends on calculation method! • Yearly compounding: $100*1.065 • Semiannual compounding: $100*1.0312 • Monthly compounding: $100*1.00560 Fabozzi Ch 2

  5. Periodic Rate Annual interest rate A r = = Number of periods in a year n Effective Rate Fabozzi Ch 2

  6. Pricing of Bonds Zero coupon bond Fabozzi Ch 2

  7. Pricing of Bonds Term structure of interest rates Fabozzi Ch 2

  8. Yield Yield = IRR = Internal Rate of Return How do we know that there is a solution? Fabozzi Ch 2

  9. Example • Price calculation: Yield calculation: Fabozzi Ch 2

  10. Price-Yield Relationship • Price and yield (of a straight bond) move in opposite directions. price yield Fabozzi Ch 2

  11. General pricing formula Fabozzi Ch 2

  12. Accrued Interest • Accrued interest = interest due in full period* • (number of days since last coupon)/ • (number of days in period between coupon payments) Fabozzi Ch 2

  13. Day Count Convention • Actual/Actual - true number of days • 30/360 - assume that there are 30 days in each month and 360 days in a year. • Actual/360 Fabozzi Ch 2

  14. Floater • The coupon rate of a floater is equal to a reference rate plus a spread. • For example LIBOR + 50 bp. • Sometimes it has a cap or a floor. Fabozzi Ch 2

  15. Inverse Floater • Is usually created from a fixed rate security. • Floater coupon = LIBOR + 1% • Inverse Floater coupon = 10% - LIBOR • Note that the sum is a fixed rate security. • If LIBOR>10% there is typically a floor. Fabozzi Ch 2

  16. Price Quotes and Accrued Interest • Assume that the par value of a bond is $1,000. • Price quote is in % of par + accrued interest • the accrued interest must compensate the seller for the next coupon. Fabozzi Ch 2

  17. Home AssignmentChapter 2 • Questions 2, 3, 7, 8, 11 Fabozzi Ch 2

  18. FRM-99, Question 17 • Assume a semi-annual compounded rate of 8% per annum. What is the equivalent annually compounded rate? • A. 9.2% • B. 8.16%C. 7.45% • D. 8% Fabozzi Ch 2

  19. FRM-99, Question 17 • (1 + ys/2)2 = 1 + y • (1 + 0.08/2)2 = 1.0816 ==> 8.16% Fabozzi Ch 2

  20. FRM-99, Question 28 • Assume a continuously compounded interest rate is 10% per annum. What is the equivalent semi-annual compounded rate? • A. 10.25% per annum. • B. 9.88% per annum. • C. 9.76% per annum. • D. 10.52% per annum. Fabozzi Ch 2

  21. FRM-99, Question 28 • (1 + ys/2)2 = ey • (1 + ys/2)2 = e0.1 • 1 + ys/2 = e0.05 • ys = 2 (e0.05 - 1) = 10.25% Fabozzi Ch 2

  22. Mortgage example • You take a mortgage $100,000 for 10 years with yearly payments and 7% interest. • What is the size of each payment? Fabozzi Ch 2

  23. Mortgage example • How much do you own bank after 3 first payments? What is the fair value of your debt if interest rates are 5%? Fabozzi Ch 2

More Related