Inflation modelling with SABR dynamics
Fabio Mercurio and Nicola Moreni introduce a new forward Consumer Price Index model that is based on a multi-factor volatility structure and leads to SABR-like dynamics for forward inflation rates. Their approach reconciles zero-coupon and year-on-year quotes, giving both fast and accurate calibration to market options data. Explicit formulas for year-on-year caps and floors are then derived in terms of the SABR volatility form. An example of calibration to market data is then provided
The inflation rates quoted in the interbank derivatives market are either zero-coupon (ZC) or year-on-year (YY), and underlie ZC and YY swaps, respectively. In a ZC swap, a fixed payment, based on the annual compounding of the quoted ZC rate, is exchanged at maturity for the inflation rate corresponding to the swap application period.1 In a YY swap, instead, payments are exchanged annually, with the floating payment that is based on the just-set annual inflation rate.
ZC and YY rates do not
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