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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/2r0.5/2
s/20.5r0.5/2
s/21r0.5/2
s/21.5r0.5/2
s/22r0.5/2 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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This document was uploaded on 02/15/2014 for the course CAREY BUSI Global Cap at Johns Hopkins.
 Spring '14

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