1. Fall-02 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html EMBAF Zvi Wiener Based on Chapter 14 in Fabozzi Bond Markets, Analysis and Strategies Analysis of Bonds with Embedded Options

2. Zvi WienerFabozzi Ch 14 slide 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.

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

4. Zvi WienerFabozzi Ch 14 slide 4 Option-Free Bond Price = present value of the cash flow discounted at spot rates. YearsYTMMarket Value 13.5%100 24.0%100 34.5%100 YearsSpot rateForward (1y) 13.500%3.500% 24.010%4.523% 34.541%5.580%

5. Zvi WienerFabozzi Ch 14 slide 5 Option-Free Bond 5.25% coupon bond with 3 years to maturity:

6. Zvi WienerFabozzi Ch 14 slide 6 r0r0 r 1,H r 1,L r 2,HH r 2,HL r 2,LL r 3,HHH r 3,HHL r 3,HLL r 3,LLL

7. Zvi WienerFabozzi Ch 14 slide 7 r0r0 r1e2r1e2 r1r1 r2e4r2e4 r3e6r3e6 r2e2r2e2 r2r2 r3e4r3e4 r3e2r3e2 r3r3

8. Zvi WienerFabozzi Ch 14 slide 8 Note that

9. Zvi WienerFabozzi Ch 14 slide 9

10. Zvi WienerFabozzi Ch 14 slide 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.

11. Zvi WienerFabozzi Ch 14 slide 11 Effective Duration P - -price if yield is decreased by  y P + -price if yield is increased by  y P 0 – initial price of the bond

12. Zvi WienerFabozzi Ch 14 slide 12 Effective Convexity

13. Zvi WienerFabozzi Ch 14 slide 13 Ch. 14: Questions 2, 7, 13, 20, 22 Home Assignment Chapter 14