Analysis of Bonds with Embedded Options

1. Analysis of Bonds with Embedded Options Zvi Wiener Based on Chapter 14 in Fabozzi Bond Markets, Analysis and Strategies http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

2. Static Spread • Yield difference is a bad measure of profitability since it does not account for term structure of IR and difference in cashflows. • Static spread: create an artificial cashflow using zero-coupon IR, then calculate the difference in yields. • See example in Exhibits 14-1, 14-2. Fabozzi Ch 14

3. Negative convexity area Callable Bond price non-callable callable yield Callable bond = noncallable – call option price Fabozzi Ch 14

4. Option-Free Bond • Price = present value of the cash flow discounted at spot rates. Years YTM Market Value 1 3.5% 100 2 4.0% 100 3 4.5% 100 Years Spot rate Forward (1y) 1 3.500% 3.500% 2 4.010% 4.523% 3 4.541% 5.580% Fabozzi Ch 14

5. Option-Free Bond • 5.25% coupon bond with 3 years to maturity: Fabozzi Ch 14

6. r3,HHH r2,HH r1,H r3,HHL r2,HL r1,L r3,HLL r2,LL r3,LLL r0 Fabozzi Ch 14

7. r3e6 r2e4 r1e2 r3e4 r2e2 r0 r1 r3e2 r2 r3 Fabozzi Ch 14

8. Note that Fabozzi Ch 14

9. Fabozzi Ch 14

10. Option-Adjusted Spread OAS • OAS is the spread over the spot rate curve that is due to the embedded options. • Modified duration often assumes fixed cashflow. • A better measure is option-adjusted or effective duration. Fabozzi Ch 14

11. Effective Duration • P- -price if yield is decreased by y • P+ -price if yield is increased by y • P0 – initial price of the bond Fabozzi Ch 14

12. Effective Convexity Fabozzi Ch 14

13. Home AssignmentChapter 14 • Ch. 14: Questions 2, 7, 13, 20, 22 Fabozzi Ch 14