Recalculating Inflation Caplet Prices with Normal Volatility

Summary

The document concerns reproducing inflation cap prices with the Bachelier formula as a step toward calibrating a SABR model. The questioner says they have normal volatility quotes by strike and maturity, a forward-rate curve, and cap prices expressed in basis points, and reports a small discrepancy between their manual calculations and the quoted prices. They ask for a full explanation of how to obtain the matching result.

No formula implementation, worked calculation, answer, or market data values are included in the document, so it does not establish the source of the discrepancy or demonstrate a pricing method. Reproduction would depend on conventions such as volatility and price units, accrual factors, discounting, caplet cash-flow timing, and whether the quoted cap price aggregates multiple caplets. Those details are not provided, which limits the document to identifying a calibration and price-reconciliation problem rather than resolving it.

Key ideas

• The task is to reprice inflation caps using normal volatilities in a Bachelier framework.
• The intended use is to support calibration of a SABR model.
• The questioner reports a small difference between calculated prices and quoted cap prices.
• The document supplies no numerical inputs, derivation, or answer that explains the discrepancy.
• Unit, discounting, accrual, and caplet aggregation conventions may affect the comparison.

Tags

# How to price an inflation caplet/floorlet using Bachelier Formula?


# How to price an inflation caplet/floorlet using Bachelier Formula?












I am trying to recalculate the prices of inflation cap in order to calibrate a SABR model. I have this table which gives me the normal volatilities values in % for the different strikes and different maturities.

I have this curve of forward rate :

And finally I have this table which gives me the cap prices in bp :

I use this function in order to recalculate the prices but I have a slight difference of a couple of bps between the prices given and the prices I obtain by manual calculation :

I know there has been a couple of questions about this but I've been stuck on this calculation for a few days if someone could help me obtain the right result with complete explanation it would be very nice !

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.