Inflation derivative

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In finance, inflation derivative (or inflation-indexed derivatives) refers to an over-the-counter and exchange-traded derivative that is used to transfer inflation risk from one counterparty to another. See Exotic derivative.

## Contents

* 1 Derivative
* 2 References
* 2.1 Citation
* 2.2 Further reading
* 3 External links

## Derivative

Typically, real rate swaps also come under this bracket, such as asset swaps of inflation-indexed bonds (government-issued inflation-indexed bonds, such as the Treasury Inflation Protected Securities, UK inflation-linked gilt-edged securities (ILGs), French OATeis, Italian BTPeis, German Bundeis and Japanese JGBis are prominent examples). Inflation swaps are the linear form of these derivatives. They can take a similar form to fixed versus floating interest rate swaps (which are the derivative form for fixed rate bonds), but use a real rate coupon versus floating, but also pay a redemption pickup at maturity (i.e., the derivative form of inflation-indexed bonds).

Inflation swaps are typically priced on a zero-coupon basis (ZC) (like ZCIIS for example), with payment exchanged at the end of the term. One party pays the compounded fixed rate and the other the actual inflation rate for the term. Inflation swaps can also be paid on a year-on-year basis (YOY) (like YYIIS for example) where the year-on-year rate of change of the price index is paid, typically yearly as in the case of most European YOY swaps, but also monthly for many swapped notes in the US market. Even though the coupons are paid monthly, the inflation rate used is still the year-on-year rate.

Options on inflation including interest rate cap and floors and straddles can also be traded. These are typically priced against YOY swaps, whilst the swaption is priced on the ZC curve.

Asset swaps also exist where the coupon payment of the linker (inflation bond) as well as the redemption pickup at maturity is exchanged for interest rate payments expressed as a premium or discount to LIBOR for the relevant bond coupon period, all dates are co-terminus. The redemption pickup is the above par redemption value in the case of par/par asset swaps, or the redemption above the proceeds notional in the case of the proceeds asset swap. The proceeds notional equals the dirty nominal price of the bond at the time of purchase and is used as the fixed notional on the LIBOR leg.

Real rate swaps are the nominal interest swap rate less the corresponding inflation swap. As for modelling, the trend has been either to provide:

* a model describing at the same time, nominal rates, real rates and inflation and representing the inflation as the exchange rate between nominal and real rates. The first type of model along these lines has been the one of Jarrow and Yildirim.
* a market model that represents the inflation like a real asset and uses similar ideas as the one of BGM to represent the inflation returns. The first type of model along these lines has been the one of Belgrade, Benhamou, Koehler[1] that is commercially available in Pricing Partners modelling suite.[2] Another more advanced version has been the one of Fabio Mercurio and Nicola Moreni.[3]

## References

### Citation

1. ↑ https://ssrn.com/abstract=576081, A Market Model for Inflation by Nabyl Belgrade, Eric Benhamou, Etienne Koehler, January 2004
2. ↑ "Pricing Partners Extends Significantly its Inflation Module with the Market Standard “BBK” Model" (in en). Derivsource. http://www.derivsource.com/articles/pricing-partners-extends-significantly-its-inflation-module-market-standard-“bbk”-model.
3. ↑ http://www.fabiomercurio.it/stochinf.pdf, Pricing Inflation Indexed options with stochastic volatility, Fabio Mercurio, Nicola Moreni, August 2005

### Further reading

* Brice Benaben; "Inflation-Linked Products: A Guide for Asset and Liability Managers" Risk Books, 2005. ISBN 1-904339-60-3.
* Deacon, Mark, Andrew Derry, and Dariush Mirfendereski; Inflation-Indexed Securities: Bonds, Swaps, and Other Derivatives (2nd edition, 2004) Wiley Finance. ISBN 0-470-86812-0.
* Brigo, Damiano and Fabio Mercurio; "Interest Rate Models -- Theory and Practice, with Smile, Inflation, and Credit" (2nd edition, 2006) Springer Finance. ISBN 3-540-22149-2.
* Canty, Paul and Markus Heider; "Inflation Markets: A Comprehensive and Cohesive Guide" (2012) Risk Books. ISBN 9781906348755.

## External links

* ISDA Inflation Derivatives Definitions
* Hughston; "Inflation Derivatives"
* Jarrow & Yildirim; "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model" Journal of Financial and Quantitative Analysis, Vol. 38, No. 2, June 2003
* Huang & Cairns; "Valuation and Hedging of LPI Liabilities"
* Hoare Capital Markets LLP
* "Savvysoft prices inflation derivatives

* v
* t
* e

Derivatives market

Derivative (finance)

Options|

| Terms|

* Credit spread
* Debit spread
* Exercise
* Expiration
* Moneyness
* Open interest
* Pin risk
* Risk-free interest rate
* Strike price
* the Greeks
* Volatility

|

Vanilla options|

* American
* Bond option
* Call
* Employee stock option
* European
* Fixed income
* FX
* Option styles
* Put
* Warrants

Exotic options|

* Asian
* Barrier
* Basket
* Binary
* Chooser
* Cliquet
* Commodore
* Compound
* Forward start
* Interest rate
* Lookback
* Mountain range
* Rainbow
* Swaption

Combinations|

* Collar
* Covered call
* Fence
* Iron butterfly
* Iron condor
* Straddle
* Strangle
* Protective put
* Risk reversal

Spreads|

* Back
* Bear
* Box
* Bull
* Butterfly
* Calendar
* Diagonal
* Intermarket
* Ratio
* Vertical

Valuation|

* Binomial
* Black
* Black–Scholes model
* Finite difference
* Garman–Kohlhagen
* Margrabe's formula
* Put–call parity
* Simulation
* Real options valuation
* Trinomial
* Vanna–Volga pricing

Swaps|

* Amortising
* Asset
* Basis
* Conditional variance
* Constant maturity
* Correlation
* Credit default
* Currency
* Dividend
* Equity
* Forex
* Forward Rate Agreement
* Inflation
* Interest rate
* Overnight indexed
* Total return
* Variance
* Volatility
* Year-on-Year Inflation-Indexed
* Zero Coupon Inflation-Indexed
* Zero Coupon Swap

* Forwards
* Futures

* Contango
* Currency future
* Dividend future
* Forward market
* Forward price
* Forwards pricing
* Forward rate
* Futures pricing
* Interest rate future
* Margin
* Normal backwardation
* Single-stock futures
* Slippage
* Stock market index future

Exotic derivatives|

* Energy derivative
* Freight derivative
* Inflation derivative
* Property derivative
* Weather derivative

Other derivatives|

* Collateralized debt obligation (CDO)
* Constant proportion portfolio insurance
* Contract for difference
* Credit-linked note (CLN)
* Credit default option
* Credit derivative
* Equity-linked note (ELN)
* Equity derivative
* Foreign exchange derivative
* Fund derivative
* Interest rate derivative
* Mortgage-backed security
* Power reverse dual-currency note (PRDC)

Market issues|

* Consumer debt
* Corporate debt
* Government debt
* Great Recession
* Municipal debt
* Tax policy

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