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

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

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

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

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15 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.

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18 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 (n 0 (t; s t ), n 3 (t; s t )) is given under each node. time0 12 3

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30 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 (n 0 (t; s t ), n 3 (t; s t )) is given under each node. time0 12 3

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39 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.

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42 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 (n 0 (t;s t ), n 3 (t;s t )) is given under each node. time0 12

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45 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 (n 0 (t;s t ), n 4 (t;s t )) is given under each node. time0 1 23

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52 Figure 13.6: An Example of a Three-Period Floorlet with a Strike. The Synthetic Floorlet Portfolio in the Money Market Account and Four-Period Zero-Coupon Bond (n 0 (t;s t ), n 4 (t;s t )) is given under each node. time0 1 23

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61 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 (n 0 (t; s t ), n 3 (t; s t )) is given under each node. time0 12 3

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