Matching OIS Curve Rates to Quoted Swap Rates

# Why is there a difference between curve swap rate and market swap rate?


# Why is there a difference between curve swap rate and market swap rate?












I am constructing an ESTR curve from inter-meeting OIS swaps (tickers EESFXA Curncy in BBG) as per below

```
import QuantLib as ql

ql.Settings.instance().evaluationDate = ql.Date(13, 12, 2024)

swap_data = [(ql.Date(13,12,2024), ql.Date(18,12,2024), 0.03167), (ql.Date(18,12,2024), ql.Date(5,2,2025), 0.02917), (ql.Date(5,2,2025), ql.Date(12,3,2025), 0.02627), (ql.Date(12,3,2025), ql.Date(23,4,2025), 0.02303)]
helpers = []
for row in swap_data:
    helpers.append(
        ql.DatedOISRateHelper(
            row[0],
            row[1],
            ql.QuoteHandle(ql.SimpleQuote(row[2])),
            ql.Estr()
        )
    )
day_count = ql.Actual360()
curve = ql.PiecewiseFlatForward(ql.Date(13, 12, 2024), helpers, day_count)
curve.enableExtrapolation()
```

When I then try to query the curve as follows

```
today = ql.Date(13, 12, 2024)
tgt = ql.TARGET()
spot = tgt.advance(today, ql.Period(2, ql.Days))
end_date = tgt.advance(spot, ql.Period('2m'))

curve.forwardRate(spot, end_date, ql.Actual360(), ql.Compounded, ql.Daily).rate()
```

I get the number to be ~2.8598

The market however prices the 2 month ESTR swap (ticker EESWEB Curncy in BBG) for those dates at ~2.8667

Why does this discrepancy appear?

## Answer by Luigi Ballabio (score 4, accepted)

https://quant.stackexchange.com/a/81408

The floating-rate leg of an OIS pays daily-compounded ESTR. The fixed-rate leg, which is the one quoted by the market, pays a simple rate. Asking for that rate gives you what you expect:

```
print(curve.forwardRate(spot, end_date, ql.Actual360(), ql.Simple).rate())
0.028667328384901276
```

However, I would be careful about asking the curve for the rate. For one thing, it wouldn't work when the fixed leg has more than one coupon; in that case, the quoted rate is not easily calculated, because it's the rate that all fixed coupons should pay for the swap to be fair, and it doesn't correspond to any one forward rate on the curve. Instead, I would instantiate the corresponding OIS and ask it for its fair rate (there's a `fairRate` method for that).

## Answer by Attack68 (score 3)

https://quant.stackexchange.com/a/81399

Its pretty easy to build a log-linearly interpolated curve in something like Excel or even on paper for these very short dated, separable and contiguous instruments. If you are uncertain if you have configured it correctly in Quantlib do a benchmark.

Here is benchmark from `rateslib`:

```
from rateslib import *  # Python 3.12, rateslib 1.6.0

curve = Curve(
    nodes={
        dt(2024, 12, 13): 1.0,
        dt(2024, 12, 18): 1.0,
        dt(2025, 2, 5): 1.0,
        dt(2025, 3, 16): 1.0,
    },
    convention="act360",
    calendar="tgt",
    id="estr"
)

solver = Solver(
    curves=[curve],
    instruments=[
        IRS(dt(2024, 12, 13), dt(2024, 12, 18), spec="eur_irs", curves="estr"),
        IRS(dt(2024, 12, 18), dt(2025, 2, 5), spec="eur_irs", curves="estr"),
        IRS(dt(2025, 2, 5), dt(2025, 3, 12), spec="eur_irs", curves="estr")
    ],
    s=[3.167, 2.917, 2.627]
)
```

With the results:

```
curve.rate(dt(2024, 12, 17), "2m")  # 2.866733
IRS(dt(2024, 12, 17), "2m", spec="eur_irs", curves="estr").rate(solver=solver)  # 2.866733
```

No idea how you are getting 2.8598.