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.923845

1.054597. .985301. 1. 1. 1.037958. 1/2. .967826. 1.016031. .984222. 1.054597. 1. 1/2. 1/2. .981381. 1.02. 1. 1. .947497. .965127. 1.059125. 1.017606. .982699. 1. .982456. 1. 1.037958. 1. 1/2. 1/2. 1/2. .960529. 1. 1.020393. B(0). .980015. 1.059125. 1. P(0,4).

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.923845

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  1. 1.054597 .985301 1 1 1.037958 1/2 .967826 1.016031 .984222 1.054597 1 1/2 1/2 .981381 1.02 1 1 .947497 .965127 1.059125 1.017606 .982699 1 .982456 1 1.037958 1 1/2 1/2 1/2 .960529 1 1.020393 B(0) .980015 1.059125 1 P(0,4) .923845 1/2 .977778 P(0,3) 1 .942322 1 = r(0) = 1.02 P(0,2) .961169 P(0,1) .980392 1.062869 P(0,0) 1 .983134 1.042854 1/2 1 1 .962414 1/2 1.019193 .981169 1.02 1/2 1.062869 1 1/2 .937148 .978637 1 .957211 1 1.022406 .978085 1 1.068337 .979870 1.042854 1 1/2 1/2 1 .953877 .976147 1.024436 1 1/2 1.068337 .974502 1 1 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.

  2. 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.

  3. 1.054597 .985301 1 1 1.037958 1/2 .967826 1.016031 .984222 1.054597 1 1/2 1/2 .981381 1.02 1 1 .947497 .965127 1.059125 1.017606 .982699 1 .982456 1 1.037958 1 1/2 1/2 1/2 .960529 1 1.020393 B(0) .980015 1.059125 1 P(0,4) .923845 1/2 .977778 P(0,3) 1 .942322 1 = r(0) = 1.02 P(0,2) .961169 P(0,1) .980392 1.062869 P(0,0) 1 .983134 1.042854 1/2 1 1 .962414 1/2 1.019193 .981169 1.02 1/2 1.062869 1 1/2 .937148 .978637 1 .957211 1 1.022406 .978085 1 1.068337 .979870 1.042854 1 1/2 1/2 1 .953877 .976147 1.024436 1 1/2 1.068337 .974502 1 1 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.

  4. (1/.967826 – 1)/2 = .016622 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. (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 2 time 0 1

  5. time 0 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.

  6. 1.054597 .985301 1 1 1.037958 1/2 .967826 1.016031 .984222 1.054597 1 1/2 1/2 .981381 1.02 1 1 .947497 .965127 1.059125 1.017606 .982699 1 .982456 1 1.037958 1 1/2 1/2 1/2 .960529 1 1.020393 B(0) .980015 1.059125 1 P(0,4) .923845 1/2 .977778 P(0,3) 1 .942322 1 = r(0) = 1.02 P(0,2) .961169 P(0,1) .980392 1.062869 P(0,0) 1 .983134 1.042854 1/2 1 1 .962414 1/2 1.019193 .981169 1.02 1/2 1.062869 1 1/2 .937148 .978637 1 .957211 1 1.022406 .978085 1 1.068337 .979870 1.042854 1 1/2 1/2 1 .953877 .976147 1.024436 1 1/2 1.068337 .974502 1 1 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.

  7. time 0 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. 1 2 3

  8. time 0 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.

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