Deriscope ## The Excel Derivatives Periscope

Zero_Inflation_Swap

The *Zero Inflation Swap* is a financial contract where one party - the inflation receiver - pays a single fixed rate coupon *Fxd* at maturity *T* and receives a single floating payment *Flt* linked to a specific inflation index from the other party - the inflation payer.

It corresponds to the Deriscope Type Inflation Swap with the setting Key Inflation Swap::Swap Type = Zero Coupon

Formally, assuming the maturity *T* can be expressed as *L(T-T₀)* number of years from the swap inception *T₀*, then:

*Fxd = N[(1+r/f)ᴸ⁽ᵀ⁻ᵀᵒ⁾ᶠ - 1]*

where *N* is the swap notional, *f* is the recompounding frequency of the fixed rate *r* and

*Flt = N[I(T-lag)/I(T₀-lag) - 1]*

where *I(t)* is the value of the referenced raw inflation index that applies at time *t*, but generally published after *t* with some index-specific publication delay *Δt*

*lag* is a contractually specified time lag that must not be less than *Δt*

Note the QuantLib implementation assumes *f = 1*

Furthermore, for dates on which no directly applicable published inflation data exist, the referenced inflation index also depends on interpolation assumptions.