In
finance, inflation derivative (or inflation-indexed derivatives) refers to an
over-the-counter
Over-the-counter (OTC) drugs are medicines sold directly to a consumer without a requirement for a prescription from a healthcare professional, as opposed to prescription drugs, which may be supplied only to consumers possessing a valid prescr ...
and exchange-traded
derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
that is used to transfer
inflation
In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduct ...
risk from one counterparty to another. See
Exotic derivatives
An exotic derivative, in finance, is a derivative which is more complex than commonly traded "vanilla" products. This complexity usually relates to determination of payoff; see option style.
The category may also include derivatives with a non- ...
.
Derivative
Typically,
real rate swaps also come under this bracket, such as
asset swap
In financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value of ownership that can ...
s of
inflation-indexed bond
Daily inflation-indexed bonds (also known as inflation-linked bonds or colloquially as linkers) are bonds where the principal is indexed to inflation or deflation on a daily basis. They are thus designed to hedge the inflation risk of a bond. Th ...
s (government-issued inflation-indexed bonds, such as the
Treasury Inflation Protected Securities, UK inflation-linked
gilt-edged securities
Gilt-edged securities are bonds issued by the UK Government. The term is of British origin, and then referred to the debt securities issued by the Bank of England on behalf of His Majesty's Treasury, whose paper certificates had a gilt (or gil ...
(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
In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations wit ...
(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 bond
Daily inflation-indexed bonds (also known as inflation-linked bonds or colloquially as linkers) are bonds where the principal is indexed to inflation or deflation on a daily basis. They are thus designed to hedge the inflation risk of a bond. Th ...
s).
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
In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduct ...
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
In marketing, a coupon is a ticket or document that can be redeemed for a financial discount or rebate when purchasing a product.
Customarily, coupons are issued by manufacturers of consumer packaged goods
or by retailers, to be used in r ...
are paid monthly, the
inflation rate
In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...
used is still the year-on-year rate.
Options on inflation including
interest rate caps,
interest rate floors and
straddle
In finance, a straddle strategy involves two transactions in options on the same underlying, with opposite positions. One holds long risk, the other short. As a result, it involves the purchase or sale of particular option derivatives that all ...
s can also be
traded. These are typically priced against YOY swaps, whilst the
swaption
A swaption is an option granting its owner the right but not the obligation to enter into an underlying swap. Although options can be traded on a variety of swaps, the term "swaption" typically refers to options on interest rate swaps.
Types of ...
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
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...
payments expressed as a
premium or
discount to
LIBOR
The London Inter-Bank Offered Rate is an interest-rate average calculated from estimates submitted by the leading banks in London. Each bank estimates what it would be charged were it to borrow from other banks. The resulting average rate is u ...
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
In financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value of ownership that can ...
. 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
The London Inter-Bank Offered Rate is an interest-rate average calculated from estimates submitted by the leading banks in London. Each bank estimates what it would be charged were it to borrow from other banks. The resulting average rate is u ...
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 that is commercially available in Pricing Partners modelling suite. Another more advanced version has been the one of Fabio Mercurio and Nicola Moreni
[http://www.fabiomercurio.it/stochinf.pdf, Pricing Inflation Indexed options with stochastic volatility, Fabio Mercurio, Nicola Moreni, August 2005]
References
Further reading
* Brice Benaben; "Inflation-Linked Products: A Guide for Asset and Liability Managers" Risk Books, 2005. .
* Deacon, Mark, Andrew Derry, and Dariush Mirfendereski; ''Inflation-Indexed Securities: Bonds, Swaps, and Other Derivatives'' (2nd edition, 2004) Wiley Finance. .
* Brigo, Damiano and Fabio Mercurio; "Interest Rate Models -- Theory and Practice, with Smile, Inflation, and Credit" (2nd edition, 2006) Springer Finance. .
* Canty, Paul and Markus Heider; "Inflation Markets: A Comprehensive and Cohesive Guide" (2012) Risk Books. .
External links
ISDA Inflation Derivatives DefinitionsHughston; "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 2003Huang & Cairns; "Valuation and Hedging of LPI Liabilities"Hoare Capital Markets LLP
{{Derivatives market
Derivatives (finance)
Interest rates
Inflation