Matching QuantLib OIS Curve Calibration and Swap Pricing

# BootStrap with quantlib USD SOFR (vs. FIXED RATE) swap curve


# BootStrap with quantlib USD SOFR (vs. FIXED RATE) swap curve












I struggle to understand why my market rates does not match my bootstrap model. So I wonder why the spread is that high between market & model.

```
maturity |  market  |   model
   1W    | 0.050640 | 0.050626
   2W    | 0.050670 | 0.050631
   3W    | 0.050720 | 0.050655
   1M    | 0.051021 | 0.050916
   2M    | 0.051391 | 0.051178
   3M    | 0.051745 | 0.051415
   4M    | 0.051940 | 0.051493
   5M    | 0.051980 | 0.051424
   6M    | 0.051820 | 0.051149
   7M    | 0.051584 | 0.050821
   8M    | 0.051310 | 0.050454
   9M    | 0.050924 | 0.049979
   10M    | 0.050604 | 0.049582
   11M    | 0.050121 | 0.049026
   12M    | 0.049550 | 0.048386
   18M    | 0.045585 | 0.044806
   2Y    | 0.042631 | 0.041774
   3Y    | 0.038952 | 0.038230
   4Y    | 0.036976 | 0.036321
   5Y    | 0.035919 | 0.035297
   6Y    | 0.035350 | 0.034745
   7Y    | 0.034998 | 0.034403
   8Y    | 0.034808 | 0.034219
   9Y    | 0.034738 | 0.034151
   10Y    | 0.034712 | 0.034125
   12Y    | 0.034801 | 0.034210
   15Y    | 0.034923 | 0.034327
   20Y    | 0.034662 | 0.034075
   25Y    | 0.033750 | 0.033193
   30Y    | 0.032826 | 0.032298
   40Y    | 0.030835 | 0.030369
   50Y    | 0.028960 | 0.028548
```

My curve only contain swaps.

Fixed leg :

- Discounting OIS

- Settlement T+2 Days

- Term 2 Week

- Day Count ACT/360

- Pay Freq Annual

- Bus Adj ModifiedFollowing

- Adjust Accrl and Pay Dates

- Roll Conv Backward (EOM)

- Calc Cal FD

- Pay Delay 2 Business Days

Float Leg

- Day Count ACT/360

- Pay Freq Annual

- Index SOFRRATE Index

- Reset Freq Daily

- Bus Adj ModifiedFollowing

```
self.swaps =   {Period("1W"): 0.05064, Period("2W"): 0.05067, Period("3W"): 0.05072, Period("1M"): 0.051021000000000004, Period("2M"): 0.051391, Period("3M"): 0.051745, Period("4M"): 0.05194, Period("5M"): 0.051980000000000005, Period("6M"): 0.051820000000000005, Period("7M"): 0.051584000000000005, Period("8M"): 0.05131, Period("9M"): 0.050924, Period("10M"): 0.050603999999999996, Period("11M"): 0.050121, Period("12M"): 0.049550000000000004, Period("18M"): 0.04558500000000001, Period("2Y"): 0.042630999999999995, Period("3Y"): 0.038952, Period("4Y"): 0.036976, Period("5Y"): 0.035919, Period("6Y"): 0.03535, Period("7Y"): 0.034998, Period("8Y"): 0.034808, Period("9Y"): 
0.034738000000000005, Period("10Y"): 0.034712, Period("12Y"): 0.034801, Period("15Y"): 0.034923, Period("20Y"): 0.034662, Period("25Y"): 0.03375, Period("30Y"): 0.032826, Period("40Y"): 0.030834999999999998, Period("50Y"): 0.02896}
```

Below is how I use `OISRateHelper`

```
rate_helpers = []
for tenor, rate in self.swaps.items():
            helper = ql.OISRateHelper(2, tenor, ql.QuoteHandle(ql.SimpleQuote(rate)), self.swap_underlying)
            rate_helpers.append(helper)
```

And below is how I compare new rates to given rates :

```
self.curve = ql.PiecewiseSplineCubicDiscount(calculation_date, rate_helpers, self.swap_day_count_conv)
yts = ql.YieldTermStructureHandle(self.curve)

# Link index to discount curve
index = index.clone(yts)

# Create engine with yield term structure
engine = ql.DiscountingSwapEngine(yts)

# Check the swaps reprice

print("maturity |  market  |   model")
for tenor, rate in self.swaps.items():
    swap = ql.MakeVanillaSwap(tenor,
                            index, 0.01,
                            ql.Period('0D'),
                            fixedLegTenor=ql.Period('2D'),
                            fixedLegDayCount=self.swap_day_count_conv,
                            fixedLegCalendar=ql.UnitedStates(ql.UnitedStates.GovernmentBond),
                            floatingLegCalendar=ql.UnitedStates(ql.UnitedStates.GovernmentBond),
                            pricingEngine=engine)

    print(f"   {tenor}    | {rate:.6f} | {swap.fairRate():.6f}")
```

Also note that :

```
self.swap_underlying = ql.OvernightIndex("USD Overnight Index", 2, ql.USDCurrency(), ql.UnitedStates(ql.UnitedStates.Settlement), ql.Actual360())

self.swap_day_count_conv = ql.Actual360()
```

Did I miss something? Is the implementation I made correct? Are there any discrepancies in the parameters?

Note Curve description :

Swap description :

## Answer by Luigi Ballabio (score 3, accepted)

https://quant.stackexchange.com/a/75657

By using `ql.MakeVanillaSwap`, you're creating a swap that pays LIBOR vs fixed, not an OIS like the ones you used to bootstrap the curve. If you actually want to use vanilla swaps, you need to use `SwapRateHelper`, not `OISRateHelper`. If you do want to use OIS instead, you'll have to use `OvernightIndexedSwap` to build the swap and retrieve the fair rate.