Pricing an Interest Rate Cap

Price interest rate caps with caplet-level breakdown, SABR volatility smile, and full Greeks using the BlueGamma API.

The /cap_floor_price endpoint prices interest rate caps (and floors) with a full caplet-level breakdown. Use this when you need to price caps programmatically, run strike/tenor scenarios, or feed cap valuations into a risk or advisory workflow.

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Basic Example: ATM Cap

Price a 3Y ATM SOFR cap on $10M notional with quarterly caplets:

import requests

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

params = {
    "index": "SOFR",
    "start_date": "0D",
    "maturity_date": "3Y",
    "cap_or_floor": "cap",
    "notional": 10000000,
    "frequency": "3M"
}

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

print(f"Strike: {data['strike_rate']:.2f}% (ATM)")
print(f"NPV: ${data['npv']:,.2f}")
print(f"Premium: {data['premium_pct']:.2f}% of notional")
print(f"Delta: {data['delta']:.2f}")
print(f"Vega: {data['vega']:.2f}")

curl -X GET "https://api.bluegamma.io/v1/cap_floor_price?index=SOFR&start_date=0D&maturity_date=3Y&cap_or_floor=cap&notional=10000000&frequency=3M" \
  -H "x-api-key: your_api_key_here"

Response (April 2026):

{
  "index": "SOFR",
  "currency": "USD",
  "type": "cap",
  "start_date": "2026-04-16",
  "maturity_date": "2029-04-16",
  "frequency": "3M",
  "notional": 10000000.0,
  "forward_rate": 3.4954,
  "strike_rate": 3.4954,
  "npv": 103164.16,
  "premium_pct": 1.0316,
  "delta": 5.6768,
  "vega": 1215.31,
  "num_caplets": 11,
  "vol_type": "sabr_calibrated",
  "sabr_rho": -0.433,
  "sabr_nu": 1.3622,
  "caplets": [
    {
      "accrual_start": "2026-07-16",
      "accrual_end": "2026-10-16",
      "forward_rate": 3.6645,
      "strike": 3.4954,
      "notional": 10000000.0,
      "normal_vol_bps": 75.67,
      "npv": 6298.32,
      "delta": 0.6717,
      "vega": 45.64,
      "discount_factor": 0.9816,
      "accrual_fraction": 0.2556
    }
  ],
  "timestamp": "2026-04-16T14:25:57"
}

ATM strike: When no strike_rate is provided, the API uses the ATM forward rate. The caplets array above shows 1 of 11 caplets for brevity.

Field	Description
npv	Net present value of the cap in the notional currency
premium_pct	NPV as a percentage of notional
strike_rate	The cap strike (ATM forward if omitted)
delta	Rate sensitivity (sum across all caplets)
vega	Volatility sensitivity (sum across all caplets)
vol_type	Volatility model used (sabr_calibrated for SOFR, flat for others)
caplets	Array of per-caplet pricing detail

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Use Case: OTM Cap with Custom Strike

Price the same cap with a 4.50% strike (out-of-the-money):

params = {
    "index": "SOFR",
    "start_date": "0D",
    "maturity_date": "3Y",
    "strike_rate": 4.5,
    "cap_or_floor": "cap",
    "notional": 10000000,
    "frequency": "3M"
}

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

curl -X GET "https://api.bluegamma.io/v1/cap_floor_price?index=SOFR&start_date=0D&maturity_date=3Y&strike_rate=4.5&cap_or_floor=cap&notional=10000000&frequency=3M" \
  -H "x-api-key: your_api_key_here"

Output (April 2026):

Strike: 4.50%
NPV: $32,025.49
Premium: 0.32% of notional

The 4.50% cap costs $32k vs $103k for ATM -- reflecting the lower probability of SOFR exceeding 4.50%.

Pricing caps for clients? Use the API to generate indicative pricing across multiple strikes and tenors in seconds.

Book a demo

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Use Case: Amortising Cap with a Notional Schedule

To price a cap on an amortising loan, send a POST request with notional as a list: one amount per caplet, in order. This example prices a 3Y quarterly SOFR cap starting in 3 months at a 4.00% strike, on $10M paying down $500k a quarter:

import requests

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

payload = {
    "index": "SOFR",
    "start_date": "3M",
    "maturity_date": "3Y",
    "strike_rate": 4.0,
    "cap_or_floor": "cap",
    "frequency": "3M",
    "notional": [10_000_000 - 500_000 * i for i in range(12)]
}

response = requests.post(url, headers=headers, json=payload)
data = response.json()

print(f"Caplets: {data['num_caplets']}")
print(f"NPV: ${data['npv']:,.2f}")

curl -X POST "https://api.bluegamma.io/v1/cap_floor_price" \
  -H "x-api-key: your_api_key_here" \
  -H "Content-Type: application/json" \
  -d '{"index": "SOFR", "start_date": "3M", "maturity_date": "3Y", "strike_rate": 4.0, "cap_or_floor": "cap", "frequency": "3M", "notional": [10000000, 9500000, 9000000, 8500000, 8000000, 7500000, 7000000, 6500000, 6000000, 5500000, 5000000, 4500000]}'

Response (October 2026):

{
  "index": "SOFR",
  "currency": "USD",
  "type": "cap",
  "start_date": "2027-01-06",
  "maturity_date": "2030-01-07",
  "frequency": "3M",
  "notional": [10000000.0, 9500000.0, 9000000.0, 8500000.0, 8000000.0, 7500000.0, 7000000.0, 6500000.0, 6000000.0, 5500000.0, 5000000.0, 4500000.0],
  "forward_rate": 4.69905,
  "strike_rate": 4.0,
  "npv": 191471.57,
  "premium_pct": 1.9147,
  "delta": 8.338844,
  "vega": 831.7,
  "num_caplets": 12,
  "caplets": [
    {
      "accrual_start": "2027-01-06",
      "accrual_end": "2027-04-06",
      "forward_rate": 4.30722,
      "strike": 4.0,
      "notional": 10000000.0,
      "normal_vol_bps": 125.35,
      "npv": 11510.09,
      "delta": 0.66313,
      "vega": 52.07,
      "discount_factor": 0.979287,
      "accrual_fraction": 0.25
    },
    {
      "accrual_start": "2027-04-06",
      "accrual_end": "2027-07-06",
      "forward_rate": 4.57401,
      "strike": 4.0,
      "notional": 9500000.0,
      "normal_vol_bps": 124.23,
      "npv": 17075.97,
      "delta": 0.726287,
      "vega": 59.52,
      "discount_factor": 0.968094,
      "accrual_fraction": 0.252778
    }
  ],
  "vol_type": "sabr_calibrated",
  "timestamp": "2026-10-06T08:36:17",
  "sabr_rho": 0.6568,
  "sabr_nu": 0.4468
}

Each caplet carries its own notional, and premium_pct is measured against the first amount in the list. The caplets array above shows 2 of 12 for brevity. To check how many amounts the schedule needs, price it once with a single notional and read num_caplets.

Mid-market price: The API returns the mid-market price, with no bank charge. A short or long first period (set by a first interest payment date) and the bank charge are available in the web app's Cap Pricer.

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Use Case: Visualising the Caplet Breakdown

Each caplet represents one reset period. Plotting NPVs and forward rates shows where value concentrates:

import requests
import matplotlib.pyplot as plt
from datetime import datetime

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

data = requests.get(url, headers=headers, params={
    "index": "SOFR", "start_date": "0D", "maturity_date": "3Y",
    "cap_or_floor": "cap", "notional": 10000000, "frequency": "3M"
}).json()

dates = [datetime.strptime(c["accrual_start"], "%Y-%m-%d") for c in data["caplets"]]
npvs = [c["npv"] for c in data["caplets"]]
forwards = [c["forward_rate"] for c in data["caplets"]]

fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 7), sharex=True)

ax1.bar(dates, npvs, width=25, color="#2563eb", alpha=0.8)
ax1.set_ylabel("Caplet NPV ($)")
ax1.set_title(f"3Y ATM SOFR Cap: {data['num_caplets']} Caplets, Total NPV ${data['npv']:,.0f}")

ax2.plot(dates, forwards, "o-", color="#2563eb", label="Forward Rate")
ax2.axhline(y=data["strike_rate"], color="#ef4444", linestyle="--", label=f"Strike ({data['strike_rate']:.2f}%)")
ax2.set_ylabel("Rate (%)")
ax2.legend()

plt.tight_layout()
plt.show()

3Y ATM SOFR cap: caplet NPVs (top) and forward rates vs strike (bottom) -- April 2026

Near-term caplets (where forwards exceed the strike) carry more intrinsic value. Later caplets derive value from time value as forwards converge toward the strike.

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Caplet Response Fields

Caplet Field	Description
accrual_start / accrual_end	The period the caplet covers
forward_rate	Implied forward rate for that period (%)
strike	The strike rate (%)
normal_vol_bps	Normal (Bachelier) implied volatility in basis points
npv	Present value of this caplet
delta	Rate sensitivity of this caplet
vega	Volatility sensitivity of this caplet
discount_factor	Discount factor to the payment date
accrual_fraction	Year fraction for the accrual period

First 4 caplets of the 3Y ATM SOFR cap (April 2026):

Period	Forward	Vol (bps)	NPV	Delta
Jul--Oct 2026	3.66%	75.67	$6,298	0.672
Oct 2026--Jan 2027	3.63%	81.89	$7,891	0.592
Jan--Apr 2027	3.59%	83.68	$7,969	0.550
Apr--Jul 2027	3.55%	85.85	$9,002	0.525

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Volatility Smile Models

The vol_smile parameter controls how implied volatility varies with strike:

Mode	Behaviour
auto (default)	SABR smile for SOFR (calibrated from market data), flat ATM vol for others
flat	ATM swaption vol for all strikes -- simpler, no skew
sabr	User-provided SABR parameters. Requires sabr_rho and sabr_nu

With auto, the response includes sabr_rho and sabr_nu so you can see the calibration used.

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Parameters

Parameter	Required	Description
index	Yes	Rate index (e.g., SOFR, SONIA, 3M EURIBOR)
start_date	Yes	Cap start date (0D for spot, or YYYY-MM-DD)
maturity_date	Yes	Cap maturity (3Y, 5Y, or YYYY-MM-DD)
strike_rate	No	Strike as percentage (e.g., 4.5). Omit for ATM
cap_or_floor	No	cap (default) or floor
notional	No	Notional amount. Default: 10,000,000. With POST, a list of amounts, one per caplet
frequency	No	Caplet frequency (1M, 3M, 6M). Default: 3M
valuation_time	No	Historical timestamp (ISO 8601) for reproducibility
vol_smile	No	auto (default), flat, or sabr
sabr_rho	No	SABR correlation (-1 to 1). Required for vol_smile=sabr
sabr_nu	No	SABR vol-of-vol (> 0). Required for vol_smile=sabr

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Related Endpoints

If you need...	Use
The underlying swap rate	/swap_rate
Forward rates for the cap period	/forward_curve
Discount factors	/discount_factor
The full swap curve	/get_swap_curve

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