Inflation Swap, Cap and Floor Model

A model is presented for pricing swaps, caps, and floors on inflation index returns. To capture general term structures of interest rates and index volatilities, the model requires time-averaged input

Pricing Inflation Swap, Cap and Floor

A model is presented for pricing swaps, caps, and floors on inflation index returns. To capture general term structures of interest rates and index volatilities, the model requires time-averaged forward rate, and volatility inputs.

For a series of reset times

we consider swap-type payments of the following form

· At maturity time

· (Zero swap)

· (Zero cap)

· (Zero floor)

· At each reset time

· (Reset swap)

· (Reset cap)

· (Reset floor)

where

· denotes the level of the inflation index at time

· denotes the reset cap (floor) return strike.

We assume that the level of the inflation index satisfies a domestic risk-neutral SDE of the form

(1)

where

· is the deterministic domestic continuously compounded risk-free,

· is a deterministic continuous dividend yield parameter,

· is a deterministic volatility parameter,

· is a standard Brownian motion.

Given SDE (1) for index levels, we may model

(2)

where

·

·

· is a standard Brownian motion.

The model

(3)

where

·

·

· is a standard Brownian motion.

We note that, in marginal distribution, Equations 2 and 3 are equivalent.

In the inflation index market, forward levels for a series of “key maturities” are traded. In particular, forward levels of the form

where

· is the domestic discount factor, at time 0, to time

· is the domestic continuously compounded risk-free rate.

Given the assumptions described in Sections 3.1 and 3.2 above, we have

and

(4)

for all

References:

https://finpricing.com/lib/FiBond.html