Constructing SOFR Forward Curves with QuantLib

# Building a forward curve for multiple tenors - Quantlib python


# Building a forward curve for multiple tenors - Quantlib python












I am attempting to build a forward curve for multiple tenors (1M / 3M / 6M / 12M) using the quantlib library. The input to my model are sofr swaps(1W through 50Y). It appears I am building my curve correctly as I can zero rates and discount factors for my spot curve directly back to bloomberg, but when I try getting forward rates I am no longer able to tie.

```
import pandas as pd
import QuantLib as ql
import math

rates = {
    '1W':5.30694,
    '2W':5.3096,
    '3W':5.3119,
    '1M':5.3155,
    '2M':5.3381,
    '3M':5.36788,
    '4M':5.39426,
    '5M':5.4169,
    '6M':5.43035,
    '7M':5.4355,
    '8M':5.43425,
    '9M':5.42945,
    '10M':5.415,
    '11M':5.39297,
    '12M':5.36985,
    '18M':5.071,
    '2Y':4.81595,
    '3Y':4.42031,
    '4Y':4.1825,
    '5Y':4.04375,
    '6Y':3.95985,
    '7Y':3.90315,
    '8Y':3.8633,
    '9Y':3.83855,
    '10Y':3.82213,
    '12Y':3.80775,
    '15Y':3.79964,
    '20Y':3.74566,
    '25Y':3.63489,
    '30Y':3.528,
    '40Y':3.31713,
    '50Y':3.11,

}

calculation_date = ql.Date(2,8,2023)
settle_time = 2

ql.Settings.instance().evaluationDate = calculation_date
yts = ql.RelinkableYieldTermStructureHandle()
index = ql.OvernightIndex("USD Overnight Index", 0, ql.USDCurrency(), ql.UnitedStates(ql.UnitedStates.Settlement), ql.Actual360(), yts)

swaps = {}
for x in rates.keys():
    swaps.update(
        {
            ql.Period(x):rates.get(x)/100
        }
    )        

#build helpers
rate_helpers = []
for tenor, rate in swaps.items():
    helper = ql.OISRateHelper(settle_time, tenor, ql.QuoteHandle(ql.SimpleQuote(rate)), index)
    rate_helpers.append(helper)

#build curve based on swap helpers
curve = ql.PiecewiseFlatForward(calculation_date, rate_helpers, ql.Actual360())
curve.enableExtrapolation()
yts.linkTo(curve)
engine = ql.DiscountingSwapEngine(yts)

#used to compare zeros and discount factors back to bloomberg
print("maturity |  market  |  model  |  zero rate  |  discount factor |  present value")

for tenor, rate in swaps.items():
    ois_swap = ql.MakeOIS(tenor, index, rate)
    pv = ois_swap.NPV()
    fair_rate = ois_swap.fairRate()
    maturity_date = ois_swap.maturityDate()
    discount_factor = curve.discount(maturity_date)
    zero_rate = -math.log(discount_factor) * 365.0/(maturity_date-calculation_date)    
    print(f"   {tenor}    | {rate*100:.6f} | {fair_rate*100:.6f} | {zero_rate*100:.6f} | {discount_factor:.6f} | {pv:.6f}")

#create monthly cadence for differrent tenors of forward rates
days = ql.MakeSchedule(curve.referenceDate(), curve.maxDate(), ql.Period('3M'))

dates,list_3mo,list_1mo,list_6mo,list_12mo = [],[],[],[],[]
for d in days:    
    forward_3mo = curve.forwardRate(
        d,
        ql.UnitedStates(ql.UnitedStates.Settlement).advance(d,90,ql.Days),
        ql.Actual365Fixed(),
        ql.Continuous,
    ).rate()
    
    forward_1mo = curve.forwardRate(
        d,
        ql.UnitedStates(ql.UnitedStates.Settlement).advance(d,30,ql.Days),
        ql.Actual365Fixed(),
        ql.Continuous,
    ).rate()
    
    forward_6mo = curve.forwardRate(
        d,
        ql.UnitedStates(ql.UnitedStates.Settlement).advance(d,ql.Period('6M')),
        ql.Actual365Fixed(),
        ql.Continuous,
    ).rate()
    
    forward_12mo = curve.forwardRate(
        d,
        ql.UnitedStates(ql.UnitedStates.Settlement).advance(d,360,ql.Days),
        ql.Actual365Fixed(),
        ql.Continuous,
    ).rate()
    
    dates.append(d)
    list_1mo.append(forward_1mo)
    list_3mo.append(forward_3mo)
    list_6mo.append(forward_6mo)
    list_12mo.append(forward_12mo)

#save output
df = pd.DataFrame(data=zip(dates,list_1mo,list_3mo,list_6mo,list_12mo),columns=('Dates','SOFR_1MO','SOFR_3MO','SOFR_6MO','SOFR_12MO'))
print(df)
df.to_csv('forward_rates.csv')
```

The dates that I return versus the screenshot are off by 2 days and the forward rates / zero rates are slightly off. Can anyone provide any insight into what some of the difference might be? The forward rates shown by bloomberg are continuous | ACT/365.