(1) Par Curve and Interpolation:
- Calculate the 3y, 4y and 7y Treasury Yields using linear interpolation (ensure formulas are in the cells)
PAR Curve | ||
Term | Yield | Bond Px |
1 | 13.00% | $100.000 |
2 | 14.00% | $100.000 |
3 | ||
4 | ||
5 | 29.00% | $100.000 |
7 | ||
10 | 70.00% | $100.000 |
Formula for the linear interpolation:
The formula is y = y1 + ((x - x1) / (x2 - x1)) * (y2 - y1),
where x is the known value,
y is the unknown value,
x1 and y1 are the coordinates that are below the known x value,
x2 and y2 are the coordinates that are above the x value.
For 3y Treasury yield:
x1 = 2
y1 = 14%
x2 = 5
y2 = 29%
x =3
y= ?
Putting in above formula:
y = 14% + ((3-2) / (5-2)) * (29%-14%) = 19%
For 4y Treasury yield:
x1 = 2
y1 = 14%
x2 = 5
y2 = 29%
x =4
y= ?
Putting in above formula:
y = 14% + ((4-2) / (5-2)) * (29%-14%) = 19%
For 7y Treasury yield:
x1 = 5
y1 = 29%
x2 = 10
y2 = 70%
x =7
y= ?
Putting in above formula:
y = 29% + ((7-5) / (10-5)) * (70%-29%) = 45.40%
Year |
Yield |
1 |
13% |
2 |
14% |
3 |
19% |
4 |
24% |
5 |
29% |
7 |
45.4% |
10 |
70% |
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