> For the complete documentation index, see [llms.txt](https://bluegamma.io/documentation/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://bluegamma.io/documentation/integrations/api/how-to-guides/fetching-zero-rates.md).

# Fetching Zero Rates

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.

***

## 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                |

{% hint style="info" %}
**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.
{% endhint %}

***

## Basic Example

```python
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())
```

```bash
curl -X GET "https://api.bluegamma.io/v1/zero_rate?index=SOFR&date=2030-12-17" \
  -H "x-api-key: your_api_key_here"
```

**Response:**

```json
{
  "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    |

***

## 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.

{% hint style="info" %}
**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`.
{% endhint %}

### Example: Value a 5-Year Amortising Loan

```python
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}")
```

```bash
# Example for a single maturity (repeat for each cash flow date)
curl -X GET "https://api.bluegamma.io/v1/zero_rate?index=SOFR&date=2028-12-17" \
  -H "x-api-key: your_api_key_here"
```

**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
```

{% hint style="success" %}
**Need this data for your valuation process?** We'll get you set up with API access. [Book a demo →](https://app.lemcal.com/@alivohra/website-demo?back=1)
{% endhint %}

***

## Use Case: Building a Zero Curve

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

```python
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}%")
```

```bash
# Example for a single date (repeat for each tenor)
curl -X GET "https://api.bluegamma.io/v1/zero_rate?index=SOFR&date=2030-12-17" \
  -H "x-api-key: your_api_key_here"
```

**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.

{% hint style="success" %}
**Ready to pull curves for your models?** Get an API key and start fetching live data in minutes.

[Get API access →](mailto:support@bluegamma.io) | [Book a demo →](https://app.lemcal.com/@alivohra/website-demo?back=1)
{% endhint %}

***

## Use Case: Comparing USD vs GBP Rates

Compare zero rates across currencies to understand relative funding costs:

```python
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")
```

```bash
# SOFR zero rate
curl -X GET "https://api.bluegamma.io/v1/zero_rate?index=SOFR&date=2030-12-17" \
  -H "x-api-key: your_api_key_here"

# SONIA zero rate
curl -X GET "https://api.bluegamma.io/v1/zero_rate?index=SONIA&date=2030-12-17" \
  -H "x-api-key: your_api_key_here"
```

**Output:**

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

***

## Visualising Zero Curves

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

<figure><img src="/files/w2eovjJkWlTRjreuAd2H" alt="Zero curve comparison chart showing SOFR and SONIA rates from 2026 to 2035"><figcaption><p>SOFR vs SONIA zero curves — live API data, December 2025</p></figcaption></figure>

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

***

## Converting Zero Rates to Discount Factors

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

```python
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:

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

***

## 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)          |

***

## 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](/documentation/integrations/available-indices.md).

***

## Related Endpoints

| If you need...                  | Use                                                                                             |
| ------------------------------- | ----------------------------------------------------------------------------------------------- |
| Discount factors directly       | [`/discount_factor`](/documentation/integrations/api/how-to-guides/getting-discount-factors.md) |
| Forward rates between two dates | [`/forward_rate`](/documentation/integrations/api/how-to-guides/getting-forward-rates.md)       |
| The full swap curve             | [`/get_swap_curve`](/documentation/integrations/api/how-to-guides/fetching-a-swap-curve.md)     |
| Historical rates                | Add `valuation_time` parameter                                                                  |

***

## 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](/documentation/integrations/excel-add-in/installation-and-setup.md) for setup instructions.

***

**Need an API key?**\
📩 <support@bluegamma.io> | 📅 [Book a call](https://app.lemcal.com/@alivohra/website-demo?back=1)


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