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.923845 .942322 .961169 .980392 1 .947497 .965127 .982699 .937148 .957211 .978085 1/2 .967826 .984222 .960529 .980015 .962414 .981169 .953877 .976147 .985301 .981381 .982456 .977778 .983134 .978637 .979870 .974502 P(0,4) P(0,3) P(0,2) P(0,1) P(0,0) = B(0) 1.02 1.037958 1.042854 r(0) = 1.02 1.017606 1.022406 1.016031 1.020393 1.019193 1.024436 1.054597 1.059125 1.062869 1.068337 time 0 1 2 3 4 Figure 14.1: An Example of a One-Factor Bond Price Curve Evolution. The Money Market Account Values and Spot Rates are Included on the Tree. Pseudo-Probabilities Are Along Each Branch of the Tree.

Figure 14.2: An Example of a European Digital Call Option's Values with Strike k = .02 and Expiration Date T = 2 on the Simple Interest Rate with Time to Maturity T* = 2. The Synthetic Option Portfolio in the Money Market Account and the Four-Period Zero-Coupon Bond (n0(t;st), n4(t;st)) Is Given Under Each Note.

.923845 .942322 .961169 .980392 1 .947497 .965127 .982699 .937148 .957211 .978085 1/2 .967826 .984222 .960529 .980015 .962414 .981169 .953877 .976147 .985301 .981381 .982456 .977778 .983134 .978637 .979870 .974502 P(0,4) P(0,3) P(0,2) P(0,1) P(0,0) = B(0) 1.02 1.037958 1.042854 r(0) = 1.02 1.017606 1.022406 1.016031 1.020393 1.019193 1.024436 1.054597 1.059125 1.062869 1.068337 time 0 1 2 3 4 Figure 14.1: An Example of a One-Factor Bond Price Curve Evolution. The Money Market Account Values and Spot Rates are Included on the Tree. Pseudo-Probabilities Are Along Each Branch of the Tree.

(1/.967826 – 1)/2 = .016622 (1/.965127 – 1)/2 = .018067* (1/.960529 – 1)/2 = .020546* (1/.961169 – 1)/2 = (1/.962414 – 1)/2 = .019527* .020200* (1/.957211 – 1)/2 = .022351 (1/.953877 – 1)/2 = .024177 time 1 2 Figure 14.3: An Example of the Evolution of a Simple Interest Rate of Maturity 2. An Asterisk "*" Denotes that the Simple Interest Rate Lies Between kl = .018 and ku = .022.

time 1 2 3 Figure 14.4: An Example of a Range Note with Maturity T = 3, Principal L = 100, Lower Bound kl = .018, Upper Bound ku = .022 on the Simple Interest Rate with Maturity T* = 2. At Each Node: The First Number is the Value (N(t;st)), the Second Number is the Cash Flow (cash flow(t;st)). The Synthetic Range Note in the Money Market Account and the Four-Period Zero-Coupon Bond (n0(t;st), n4(t;st)) is Given Under Each Node.

.923845 .942322 .961169 .980392 1 .947497 .965127 .982699 .937148 .957211 .978085 1/2 .967826 .984222 .960529 .980015 .962414 .981169 .953877 .976147 .985301 .981381 .982456 .977778 .983134 .978637 .979870 .974502 P(0,4) P(0,3) P(0,2) P(0,1) P(0,0) = B(0) 1.02 1.037958 1.042854 r(0) = 1.02 1.017606 1.022406 1.016031 1.020393 1.019193 1.024436 1.054597 1.059125 1.062869 1.068337 time 0 1 2 3 4 Figure 14.1: An Example of a One-Factor Bond Price Curve Evolution. The Money Market Account Values and Spot Rates are Included on the Tree. Pseudo-Probabilities Are Along Each Branch of the Tree.

time 1 2 3 Figure 14.5: An Example of the Cash Flows from an Index Amortizing Swap with Maturity T = 3, Initial Principal L0 = 100, Lockout Period T* = 1, Which Amortizes 50 Percent of the Principal if r(t;st) < 1.018.

time 1 2 3 Figure 14.6: An Example of an Index Amortizing Swap with Maturity T = 3, Initial Principal L0 = 100, Lockout Period T* = 1, Which Amortizes 50 Percent of the Principal if r(t;st) < 1.018. The First Number is the Value, the Second is the Cash Flow. The Synthetic Index Amortizing Swap Portfolio in the Money Market Account and Three-Period Zero-Coupon Bond (n0(t;st), n3(t;st)) is Given Under Each Node.