1. Fall-01 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html FIBI Zvi Wiener 02-588-3049 mswiener@mscc.huji.ac.il Fixed Income Instruments 6

2. Zvi WienerFIFIBI - 6 slide 2 IR derivatives Forward and Futures Options Caps, Floors Swaps Structured notes Hedging Mathematical models

3. Zvi WienerFIFIBI - 6 slide 3 Interest rate futures Legal agreement settlement, delivery date quantity and quality of deliverable asset futures price (it is NOT a price!) long and short positions margin requirements

4. Zvi WienerFIFIBI - 6 slide 4 Margin requirements Initial margin Maintenance margin - margin call trigger Variation margin - after a margin call Mark to market procedure reduces counterparty risk!

5. Zvi WienerFIFIBI - 6 slide 5 Marking to Market Your balance time Initial margin Maint. margin margin call

6. Zvi WienerFIFIBI - 6 slide 6 Futures Contract T-Bills T-Notes T-Bonds notional is typically $100,000 deliverable bond is unknown, CTD option timing option (during the delivery month) wild card option

7. Zvi WienerFIFIBI - 6 slide 7 Options This type of contract is an obligation of one side only, but it requires a payment to purchase the right to choose.

8. Zvi WienerFIFIBI - 6 slide 8 Call Value before Expiration E. Call XUnderlying

9. Zvi WienerFIFIBI - 6 slide 9 Put Value before Expiration E. Put XUnderlying premium X

10. Zvi WienerFIFIBI - 6 slide 10 IR Options Call Put European American Bermudian Exotic: Asian, Digital, Knock-In, Knock-Out, path dependent and multiple asset options.

11. Zvi WienerFIFIBI - 6 slide 11 Various IR Options Futures options Caps Floors Exchange options Swaptions

12. Zvi WienerFIFIBI - 6 slide 12 Cap Is priced as a sequence of caplets time cap

13. Zvi WienerFIFIBI - 6 slide 13 Floor time floor

14. Zvi WienerFIFIBI - 6 slide 14 Collar time floor cap

15. Zvi WienerFIFIBI - 6 slide 15 Option pricing Time value, intrinsic value underlying time to maturity interest rates strike coupons volatility

16. Zvi WienerFIFIBI - 6 slide 16 Swaps Currency swap Interest rate swap Amortizing swap Swaption

17. Zvi WienerFIFIBI - 6 slide 17 Currency swap

18. Zvi WienerFIFIBI - 6 slide 18 Currency Swap 300Y300Y300Y300Y300Y300Y 10,000Y $5$5$5$5$5$5 $100

19. Zvi WienerFIFIBI - 6 slide 19 IR swap

20. Zvi WienerFIFIBI - 6 slide 20 IR Swap 333333333333 100 L+1L+1L+1L+1L+1L+1 100

21. Zvi WienerFIFIBI - 6 slide 21 IR Swap L+1L+1L+1L+1L+1L+1 100 111111111111 + a regular LIBOR loan for one year!

22. Zvi WienerFIFIBI - 6 slide 22 Term Structure Models Binomial trees Short-term based analytical models LIBOR based analytical models Multi-factor models Simulations

23. Zvi WienerFIFIBI - 6 slide 23 Binomial Trees 6% 6.5% 5.5% 7% 6% 5% 7.5% 6.5% 5.5% 4.5%

24. Zvi WienerFIFIBI - 6 slide 24 6% 6.5% 5.5% 7% 6% 5% 7.5% 6.5% 5.5% 4.5% 83.97 88.2 89.8 93 94 95 100 Interest rates Bond prices

25. Zvi WienerFIFIBI - 6 slide 25 Typical yield curves time to maturity yield increasing decreasing humped

26. Zvi WienerFIFIBI - 6 slide 26 Analytic Term Structure Models

27. Zvi WienerFIFIBI - 6 slide 27 Analytic Term Structure Models Hull, White Black-Karasinsky Black-Derman-Toy Heath-Jarrow-Morton Affine TS modles Gaussian models

28. Zvi WienerFIFIBI - 6 slide 28 Arithmetic BM dX =  dt +  dW   time X

29. Zvi WienerFIFIBI - 6 slide 29 Geometric BM dX =  Xdt +  XdW time X

30. Zvi WienerFIFIBI - 6 slide 30 Mean Reverting Process dX =  (  -X)dt +  X  dW time X 

31. Zvi WienerFIFIBI - 6 slide 31 Ho and Lee Model Rates are normally distributed. All rates have the same variability. The model has an analytic solution.

32. Zvi WienerFIFIBI - 6 slide 32 Bond Prices under Ho and Lee Where

33. Zvi WienerFIFIBI - 6 slide 33 Option Prices under Ho and Lee A discount bond matures at s, a call option matures at T

34. Zvi WienerFIFIBI - 6 slide 34 Monte Carlo

35. Zvi WienerFIFIBI - 6 slide 35 Monte Carlo Simulation

36. Zvi WienerFIFIBI - 6 slide 36 Callable Bond Payoff Straight Debt Debt Callable Bond Value of the firm’s call option

37. Zvi WienerFIFIBI - 6 slide 37 Convertible Bond Payoff Stock Straight Bond Convertible Bond

38. Zvi WienerFIFIBI - 6 slide 38 Protective Put Payoff XUnderlying X Put Protective Put Stock

39. Zvi WienerFIFIBI - 6 slide 39 Covered Call Payoff X X Written Call Covered Call Stock

40. Zvi WienerFIFIBI - 6 slide 40 Straddle Payoff X X Straddle Call Put