Fetching Zero Rates

Fetch zero-coupon rates for discounting cash flows, building DCF models, and valuing debt portfolios.

The /zero_rate endpoint returns the zero-coupon rate (spot rate) for any date and index. Use this when you need to discount future cash flows to present value.

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When to Use Zero Rates

Use Case	Why Zero Rates?
Discount cash flows in a DCF model	Zero rates give you the pure time-value of money for each maturity
Value a loan or bond portfolio	Calculate the present value of future principal and interest payments
Build a pricing engine	Zero rates are the foundation for swap, bond, and derivative pricing
Compare rates across tenors	Unlike swap rates, zero rates can be directly compared

Zero rates vs swap rates: Swap rates are averages across the life of the swap. Zero rates represent the rate for a specific maturity — no coupon effects.

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Basic Example

import requests

url = "https://api.bluegamma.io/v1/zero_rate"
headers = {"x-api-key": "your_api_key"}

params = {
    "index": "SOFR",
    "date": "2030-12-17"  # 5 years from now
}

response = requests.get(url, headers=headers, params=params)
print(response.json())

Response:

{
  "index": "SOFR",
  "date": "2030-12-17",
  "valuation_time": "2025-12-17T11:47:29.268475",
  "zero_rate": 3.71,
  "day_count": "Actual360",
  "compounding": "Simple",
  "timestamp": "2025-12-17T11:46:57"
}

Field	Description
zero_rate	The zero-coupon rate as a percentage (3.71%)
day_count	Day count convention used (Actual/360 for SOFR)
compounding	Compounding convention (Simple for OIS indices)
timestamp	When the underlying market data was captured

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Use Case: Discounting Cash Flows

A common task is discounting a series of future cash flows to present value — for example, valuing a loan with scheduled repayments.

Simple compounding: The API returns zero rates with simple compounding, so the discount factor formula is DF = 1 / (1 + rate × time), not 1 / (1 + rate)^time.

Example: Value a 5-Year Amortising Loan

import requests

url = "https://api.bluegamma.io/v1/zero_rate"
headers = {"x-api-key": "your_api_key"}

# Loan cash flows (principal + interest payments)
cash_flows = [
    {"date": "2026-12-17", "amount": 220000},  # Year 1
    {"date": "2027-12-17", "amount": 215000},  # Year 2
    {"date": "2028-12-17", "amount": 210000},  # Year 3
    {"date": "2029-12-17", "amount": 205000},  # Year 4
    {"date": "2030-12-17", "amount": 200000},  # Year 5
]

total_pv = 0

for cf in cash_flows:
    # Get the zero rate for this maturity
    response = requests.get(url, headers=headers, params={
        "index": "SOFR",
        "date": cf["date"]
    })
    zero_rate = response.json()["zero_rate"] / 100
    
    # Calculate years to maturity (simplified)
    years = int(cf["date"][:4]) - 2025
    
    # Discount using simple compounding (as returned by the API)
    discount_factor = 1 / (1 + zero_rate * years)
    pv = cf["amount"] * discount_factor
    total_pv += pv
    
    print(f"{cf['date']}: £{cf['amount']:,} × {discount_factor:.4f} = £{pv:,.0f}")

print(f"\nTotal Present Value: £{total_pv:,.0f}")

Output:

2026-12-17: £220,000 × 0.9664 = £212,608
2027-12-17: £215,000 × 0.9365 = £201,348
2028-12-17: £210,000 × 0.9059 = £190,239
2029-12-17: £205,000 × 0.8750 = £179,375
2030-12-17: £200,000 × 0.8436 = £168,720

Total Present Value: £952,290

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Use Case: Building a Zero Curve

Fetch zero rates across multiple tenors to build a complete curve:

import requests

url = "https://api.bluegamma.io/v1/zero_rate"
headers = {"x-api-key": "your_api_key"}

tenors = ["2026-12-17", "2027-12-17", "2028-12-17", "2029-12-17", 
          "2030-12-17", "2031-12-17", "2032-12-17"]

zero_curve = []

for date in tenors:
    response = requests.get(url, headers=headers, params={
        "index": "SOFR",
        "date": date
    })
    data = response.json()
    zero_curve.append({
        "date": date,
        "zero_rate": data["zero_rate"]
    })

# Print the curve
for point in zero_curve:
    print(f"{point['date']}: {point['zero_rate']:.2f}%")

Current SOFR Zero Curve (December 2025):

Maturity	Zero Rate
Dec 2026 (1Y)	3.48%
Dec 2027 (2Y)	3.39%
Dec 2028 (3Y)	3.46%
Dec 2029 (4Y)	3.57%
Dec 2030 (5Y)	3.71%
Dec 2031 (6Y)	3.87%
Dec 2032 (7Y)	4.03%

The curve is slightly inverted at the short end (1Y > 2Y), then steepens — reflecting market expectations of near-term rate cuts followed by normalisation.

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Use Case: Comparing USD vs GBP Rates

Compare zero rates across currencies to understand relative funding costs:

import requests

url = "https://api.bluegamma.io/v1/zero_rate"
headers = {"x-api-key": "your_api_key"}

date = "2030-12-17"  # 5-year maturity

# Fetch USD (SOFR) and GBP (SONIA) zero rates
sofr = requests.get(url, headers=headers, params={"index": "SOFR", "date": date}).json()
sonia = requests.get(url, headers=headers, params={"index": "SONIA", "date": date}).json()

print(f"5Y SOFR Zero Rate:  {sofr['zero_rate']:.2f}%")
print(f"5Y SONIA Zero Rate: {sonia['zero_rate']:.2f}%")
print(f"Spread (SONIA - SOFR): {(sonia['zero_rate'] - sofr['zero_rate']) * 100:.0f} bps")

Output:

5Y SOFR Zero Rate:  3.71%
5Y SONIA Zero Rate: 3.94%
Spread (SONIA - SOFR): 23 bps

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Visualising Zero Curves

By fetching zero rates across multiple tenors, you can build and visualise complete zero curves:

SOFR vs SONIA zero curves — live API data, December 2025

The chart shows:

• SOFR (USD): Slight inversion at the short end (1Y > 2Y), then steepening to ~4.6% at 10Y

• SONIA (GBP): Consistently 20-30bps higher across all tenors

• Both curves reflect market expectations of near-term rate cuts followed by normalisation

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Converting Zero Rates to Discount Factors

The API returns zero rates with simple compounding. To convert to a discount factor:

zero_rate = 3.71 / 100  # 3.71%
years = 5

# Simple compounding formula (matches API convention)
discount_factor = 1 / (1 + zero_rate * years)
print(f"Discount Factor: {discount_factor:.6f}")  # 0.843282

Or use the /discount_factor endpoint directly to skip the calculation:

curl "https://api.bluegamma.io/v1/discount_factor?index=SOFR&date=2030-12-17" \
  -H "x-api-key: your_api_key"

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Parameters

Parameter	Required	Description
index	Yes	The interest rate index (e.g., SOFR, SONIA, 6M EURIBOR)
date	Yes	The maturity date (YYYY-MM-DD format)
valuation_time	No	Historical timestamp for the curve (ISO 8601 format)

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Supported Indices

Index	Currency	Day Count
SOFR	USD	Actual/360
SONIA	GBP	Actual/365
ESTR	EUR	Actual/360
6M EURIBOR	EUR	Actual/360
CORRA	CAD	Actual/365

For the full list, see Available Indices.

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Related Endpoints

If you need...	Use
Discount factors directly	/discount_factor
Forward rates between two dates	/forward_rate
The full swap curve	/get_swap_curve
Historical rates	Add valuation_time parameter

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Excel Alternative

If you prefer Excel, use the BlueGamma Add-in:

=BlueGamma.ZERO_RATE("SOFR", "2030-12-17")

Returns: 3.71

See Excel Add-in Guide for setup instructions.

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