Inflation derivatives: models and methods

Last updated 10 November 2026

This page describes how GIAnalyzer and the Gamma Impact API value inflation derivatives and measure their risk: zero-coupon inflation swaps and real rate swaps, how the consumer price index is projected, and what the models do not do. It describes GIAnalyzer version 5.12.0; the Gamma Impact API covers the same instruments and models. It is provided for information and is not a contractual specification.

The function-level detail is in the function reference.

Indexation

• Base index: the CPI level at the trade's inception, given as an input.
• Reference index for a cash flow: the projected CPI of the month a set number of months before the payment date (the indexation lag). The lag is a whole number of months, set separately for the valuation date and for the cash flows.
• An inflation-linked cash flow is the nominal amount multiplied by the ratio of the reference index to the base index.

Projecting the index

The projected index comes from an expected CPI curve: dates and index levels, starting from the last published CPI on the valuation date.

• Within the first year, when the curve is given month by month, the projected index for a month is the curve's level for that month.
• Beyond it, the curve is read at yearly points. Between two points, the average monthly inflation rate is implied, and the index is compounded month by month from the last point, with a seasonal adjustment for each calendar month: twelve monthly corrections to the average rate, given as inputs.
• Beyond the last point, the last average monthly inflation rate is held constant.

Instruments and models

Zero-coupon inflation swaps

One payment at maturity on each side, in either direction:

• Inflation leg: the notional times the ratio of the reference index at maturity to the base index, less the notional unless the notional is exchanged.
• Fixed leg: the notional compounded annually at the fixed rate over the life of the swap, less the notional unless it is exchanged.
• Both are discounted on the nominal discounting curve.
• Price is the fixed rate that makes the swap worth zero: the zero-coupon breakeven inflation rate.

Real rate swaps

An inflation-linked leg against a nominal leg, fixed or floating, in all four directions (paying or receiving inflation):

• Inflation leg: a real coupon on the indexed notional: each coupon is the real rate on the outstanding notional over the period, times the index ratio at its payment date. Principal repayments are indexed at their own dates.
• Nominal leg: a fixed or floating leg valued as in an interest rate swap (see Interest rate derivatives), floating legs on IBOR or overnight rates.
• Notional exchanges at the start and at maturity, as specified.
• Amortization: bullet, regular amortization, or a custom schedule of principal dates and amounts.
• The two legs may be in different currencies, converted at the spot exchange rate.

Risk measures

All sensitivities are computed by revaluing the swap with a small change in one input (finite differences).

What the models do not do

The inflation models:

• use whole-month indexation lags, with no daily interpolation between monthly index prints;
• apply no deflation floor: a fall in the index reduces the inflation leg below par;
• cover no inflation options (caps and floors), no year-on-year inflation swaps, and no inflation-linked bond pricing;
• take the expected CPI curve as given: they do not build it from market breakeven quotes.

References

• Brigo, D. and Mercurio, F. (2006). Interest Rate Models: Theory and Practice, 2nd edition, chapters on inflation. Springer.
• Deacon, M., Derry, A. and Mirfendereski, D. (2004). Inflation-Indexed Securities, 2nd edition. Wiley.
• Kerkhof, J. (2005). Inflation Derivatives Explained. Lehman Brothers Fixed Income Quantitative Research.

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