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Table 13.2: Cash Flow to a Fixed Rate Loan with Coupon C, Principal L, and maturity date T.

Table 13.1: Cash Flow from a Floating Rate Loan of a dollar (the Principal), with maturity date T. Table 13.2: Cash Flow to a Fixed Rate Loan with Coupon C, Principal L, and maturity date T. Figure 13.1: An Illustration of a Swap Changing a Fixed Rate Loan into a Floating Rate Loan.

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Table 13.2: Cash Flow to a Fixed Rate Loan with Coupon C, Principal L, and maturity date T.

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  1. Table 13.1: Cash Flow from a Floating Rate Loan of a dollar (the Principal), with maturity date T.

  2. Table 13.2: Cash Flow to a Fixed Rate Loan with Coupon C, Principal L, and maturity date T.

  3. Figure 13.1: An Illustration of a Swap Changing a Fixed Rate Loan into a Floating Rate Loan

  4. Table 13.3: The Cash Flows and Values from a Swap Receiving Fixed and Paying Floating

  5. 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 13.2: 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.

  6. time 0 1 2 3 Figure 13.3: An Example of a Swap Receiving Fixed and Paying Floating with Maturity Time 3, Principal $100, and Swap Rate .02. Given first is the swap's value, then the swap's cash flow. The synthetic swap portfolio in the money market account and three-period zero-coupon bond (n0(t; st), n3(t; st)) is given under each node.

  7. time 0 1 2 3 Figure 13.3: An Example of a Swap Receiving Fixed and Paying Floating with Maturity Time 3, Principal $100, and Swap Rate .02. Given first is the swap's value, then the swap's cash flow. The synthetic swap portfolio in the money market account and three-period zero-coupon bond (n0(t; st), n3(t; st)) is given under each node.

  8. 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 13.2: 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.

  9. Figure 13.4: An Example of a Two-Period Caplet with a 1.02 Strike. The synthetic caplet portfolio in the money market account and three-period zero-coupon bond (n0(t;st), n3(t;st)) is given under each node. time 0 1 2

  10. Figure 13.5: An Example of a Three-Period Caplet with a 1.02 Strike. The Synthetic Caplet Portfolio in the Money Market Account and Four-Period Zero-Coupon Bond (n0(t;st), n4(t;st)) is given under each node. time 0 1 2 3

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