Sampling Discount Factors from an Interpolated Yield Curve
Summary
The document shows how to obtain discount factors at dates between the quoted maturities used to build a QuantLib discount curve. After constructing a piecewise log-linear discount curve from swap-rate inputs, the example generates a sequence of future dates and calls the curve’s discount method for each one. The resulting values form a regularly spaced sample of the curve, which can be displayed alongside the dates.
The example code samples at five-year intervals, although the question asks for half-year intervals; the same approach applies by choosing dates six months apart. A second answer clarifies the central point: the curve can return a discount factor for any requested date, so there is no need to limit output to the original curve nodes. The example uses synthetic Swedish krona swap data and enables extrapolation beyond the last input tenor. Its output therefore illustrates API usage rather than providing market evidence, and extrapolated values depend on the curve’s assumptions and configuration.
Key ideas
- A constructed discount curve can return discount factors for dates between its input maturity nodes.
- Choose the desired date spacing and query the curve once for each date.
- The example samples at five-year steps, while half-year sampling can be produced by changing the date increment.
- Discount factors beyond the last curve node may rely on extrapolation settings and should be interpreted accordingly.
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Full text
# QuantLib Python - Discount Factor Interpolation within curve nodes
# QuantLib Python - Discount Factor Interpolation within curve nodes
Generated a discount curve, dCurve.PiecewiseLogLinearDiscount() using input par rate for terms (.5Y, 1Y, 2Y, 3Y, 5Y, 7Y, 10Y, 15Y, 20Y, 30Y) and output discount curve matching the input term structure. Any suggestions on how to output the discount factor curve on a .5Y interval term structure up to 30Y?
## Answer by Xiarpedia (score 1)
https://quant.stackexchange.com/a/77563
Based on your question I created the following curve example:
```
import QuantLib as ql
import pandas as pd
# Set the evaluation date
ql.Settings.instance().evaluationDate = ql.Date(30, 12, 2022)
# Declare a store variable for the helpers
helpers = []
# Create the attributes of the swap
calendar = ql.Sweden()
frequency = ql.Annual
convention = ql.ModifiedFollowing
# Synthetic market data
daycount = ql.Thirty360(ql.Thirty360.BondBasis)
index = ql.IborIndex(
"MyIndex",
ql.Period("3M"),
2,
ql.SEKCurrency(),
calendar,
ql.Following,
False,
daycount,
)
tenor = ["4Y", "5Y", "6Y", "7Y", "8Y", "9Y", "10Y", "12Y", "15Y", "20Y", "25Y", "30Y"]
quotes = [
3.33,
3.2775,
3.235,
3.205,
3.1775,
3.1525,
3.1325,
3.095,
3.0275,
2.92,
2.815,
2.6925,
]
for r, m in zip(quotes, tenor):
rate = ql.QuoteHandle(ql.SimpleQuote(r / 100.0))
tenor = ql.Period(m)
helpers.append(
ql.SwapRateHelper(
rate, tenor, calendar, frequency, convention, daycount, index
)
)
curve = ql.PiecewiseLogLinearDiscount(0, calendar, helpers, ql.Actual365Fixed())
curve.enableExtrapolation()
dates, rates = zip(*curve.nodes())
```
Which leaves me at the stage you are at. We can then interpolate on a 5 year interval as following:
```
# Interpolate on a 5Y interval
nodes = []
start_date = ql.Date(30, 12, 2022)
while True:
start_date += ql.Period("5Y")
nodes.append(start_date)
if start_date > ql.Date(30, 12, 2053):
break
discount_factors = [curve.discount(d) for d in nodes]
display(pd.DataFrame(dict({"Date": nodes, "Discount Factor": discount_factors})))
```
Which results in:
| | Date | Discount Factor |
| 0 | December 30th, 2027 | 0.851205 |
| 1 | December 30th, 2032 | 0.735589 |
| 2 | December 30th, 2037 | 0.641855 |
| 3 | December 30th, 2042 | 0.567462 |
| 4 | December 30th, 2047 | 0.508218 |
| 5 | December 30th, 2052 | 0.464726 |
| 6 | December 30th, 2057 | 0.424997 |
## Answer by Luigi Ballabio (score 0)
https://quant.stackexchange.com/a/77564
You can pass any date you like to the `discount` method of the curve you built. It will return the corresponding discount factor.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.