© K. Cuthbertson and D. Nitzsche Figures for Chapter 18 PRICING INTEREST RATE DERIVATIVES (Financial Engineering : Derivatives and Risk Management)

© K. Cuthbertson and D. Nitzsche Figure 18.1 : Timing of option payoff 0TT*T* Expiry\Payoff for the option Actual Cash Payout r r*r*

© K. Cuthbertson and D. Nitzsche Figure 18.2 : Payer swaption 0T+nT+n Expiry of swaption T (T+1/m) (T+2/m) (T+4/m)(T+3/m) Swap rate at expiry = cp T K = strike rate m= number of payments pa in swaption (= 4 here) n= number of years in the swap Q = notional principal in the swap If cp T > K at expiry then the payer swaption has positive cash flows every m-periods of (Q/m) {cp T - K},until time T+n.

© K. Cuthbertson and D. Nitzsche Figure 18.3 : Short rate lattice r(0,1)=5 VuVu VdVd V uu V dd V ud r(0,1) = 5% r(0,2) = 6% r u (1,2)=8.41 r d (1,2)=5.64 r uu (2,3)=12.84 r ud (2,3)=8.78 r dd (2,3)=6.01 r 2du, (3,4)=8.96 r 3d (3,4)=6.25 Time r 2ud, (3,4)=12.84 r 3u, (3,4)=18.4 (1-q) q r 4d = 6.46 r 3du = 9.07 r 2d2u = r 1d3u = r 4u = 25.15

© K. Cuthbertson and D. Nitzsche Figure 18.4 : Short rate lattice, r t,i Index, i Time, t 1,02,03,04,0 0,0 1,1 2,2 3,3 4,4 2,13,14,1 3,24,2 4,

© K. Cuthbertson and D. Nitzsche Figure 18.5 : Trinominal lattice 0 12 A 12% B C D 14% 12% 10% 16% (4%) 14% (2%) 12% (0%) 10% (0%) 8% (0%) E Time

© K. Cuthbertson and D. Nitzsche Figure A18.1 : Term structure : interest rates lattice 012 r 00 (0,1) r 1u (1,2) r 1d (1,2) Time f 00 (1,2) f 00 (1,3) r 1u (1,3) f 1u (2,3) r 1d (1,3) f 1d (2,3) r 2uu (2,3) r 2ud (2,3) r 2dd (2,3)