Global Capital Market-HMW2

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Unformatted text preview: rms: Time (years) 0.5 1 1.5 2 2.5 3 Spot Rate 2.6507% 2.9197% 3.0000% 3.1049% 3.2299% 3.3400% 2. From the theorem of No Arbitrage, we have ( ( ) ) ( ) ( ) ( ) ( [ ) Where denotes the forward rate for borrowing and lending that starts in n years and lasts for m years; denotes the spot rate lasting for n years, denotes the spot rate lasting for n+m years. ), the result is as follows: 3. All possible forward rate has been calculated ( m 0.5 1 1.5 2 2.5 n 0.5 3.1891% 3.1749% 3.2566% 3.3750% 3.4781% 1 3.1607% 3.2903% 3.4370% 3.5504% N/A 1.5 3.4199% 3.5753% 3.6804% N/A N/A 2 3.7307% 3.8108% N/A N/A N/A 2.5 3.8909% N/A N/A N/A N/A (Just using the general formula of (2) with specific n and m to calculate each forward rate) 4. The steps are as follows: ① construct the table showing fixed payment and expected floating payment Time 0 0.5 1 1.5 2 2.5 Spot Rate fixed payment Expected floating rate Net payment 2.6507% 2.9197% 3.0000% 3.1049% 3.2299% s/2 s/2 s/2 s/2 s/2 r0.5/2 0.5r0.5/2 1r0.5/2 1.5r0.5/2 2r0.5/2 s/2-r0.5/2 s/2-0.5r0.5/2 s/2-1r0.5/2 s/2-1.5r0.5/2 s/2-2r0.5/2 ② Referring the data we have: r0.5/2 2.6507% 0.5r0.5/2 1r0.5/2 1.5r0.5/2 3.1891% 3.1607% 2r0.5/2 3.4199% 3.7307% ③ By setting the NPV of the Net payment be zero, we derive the value of s ∑ ( ⁄) Therefore, the 2.5 years swap rate is roughly 3.2223% ( )...
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