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Choosing Bachelier or Black Pricing for Long-Dated USD Rate Caps

Article Quant Q&A · Author: ExcelRates
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Summary

This question asks whether to price caplets on one-month USD floating rates with a normal Bachelier model or a lognormal Black model. The instruments are caps intended to limit rate exposure on pay-floating, receive-fixed swaps, with floating payments floored at zero by the contract. The author considers out-of-the-money strikes and maturities extending to long tenors, and mentions rates such as LIBOR or SOFR.

The post identifies modeling choices that matter for an interest-rate derivatives problem: the distributional assumption for the underlying rate, the contractual floor, and the maturity and strike profile. However, it provides no answer, pricing comparison, market inputs, volatility convention, or calibration details. It therefore does not establish which model is appropriate or how the payment floor affects valuation. The content is a useful framing of a caplet-model selection question, but not a practical recommendation or evidence-based comparison.

Key ideas

  • The question compares normal Bachelier and lognormal Black pricing for USD rate caplets.
  • The underlying floating payment is contractually floored at zero.
  • The proposed caps have out-of-the-money strikes and maturities that may extend to long tenors.
  • No model recommendation, calibration method, or pricing evidence is provided.

Tags

OptionsFixed incomeDerivatives pricing
Full text
# Which Model Should I Use for Pricing USD Interest Rate Caps (7, 10, 30 year maturities) on 1Month Rates?


# Which Model Should I Use for Pricing USD Interest Rate Caps (7, 10, 30 year maturities) on 1Month Rates?












I am trying to price USD interest rate caps on 1M rates (e.g., LIBOR, SOFR, etc.).

The caps are designed to limit the exposure on non-callable USD Pay Float / Receive fixed positions in interest rate swaps. The swaps legal documentation states that the minimum float rate will alway be zero. If the USD float index (e.g., 1M SOFR) is -0.25, the float payment will be calculated at 0.00.

The strike rate on the caps is out-of-the money (e.g., 3%, 4%, 5%). And the maturities of the caps can extend as far as 30 years.

Should I use a NORMAL (Bachelier) or the standard LOGNORMAL (Black 76) for pricing the caplets?

Thanks in advance.

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