finance Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...

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 pres ...

derivative In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is t ...

inflation In economics, inflation is an increase in the average price of goods and services in terms of money. This increase is measured using a price index, typically a consumer price index (CPI). When the general price level rises, each unit of curre ...

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. T ...

gilt-edged securities Gilt-edged securities, also referred to as gilts, are bonds issued by the UK Government. The term is of British origin, and referred to the debt securities issued by the Bank of England on behalf of His Majesty's Treasury, whose paper certifi ...

Inflation swap An inflation swap is an agreement between two counterparty, counterparties to swap fixed rate payments on a notional principal amount for floating rate payments linked to an inflation index, such as the consumer price index.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 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. T ...

s).

Inflation swap An inflation swap is an agreement between two counterparty, counterparties to swap fixed rate payments on a notional principal amount for floating rate payments linked to an inflation index, such as the consumer price index.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 average price of goods and services in terms of money. This increase is measured using a price index, typically a consumer price index (CPI). When the general price level rises, each unit of curre ...

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 ...

are paid monthly, the

inflation In economics, inflation is an increase in the average price of goods and services in terms of money. This increase is measured using a price index, typically a consumer price index (CPI). When the general price level rises, each unit of curre ...

rate used is still the year-on-year rate. Options on inflation including interest rate cap and 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 al ...

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 T ...

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 (Libor ) was an interest rate average calculated from estimates submitted by the leading Bank, banks in London. Each bank estimated what it would be charged were it to borrow from other banks. It was the prim ...

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 ::''See Notional amount or Notional profit for economic terms '' Notional (born February 1, 2004, in California) is a retired American Thoroughbred racehorse. He was sired by In Excess and out of the mare Truly Blessed. His damsire, French Depu ...

in the case of the proceeds asset swap. The proceeds

notional ::''See Notional amount or Notional profit for economic terms '' Notional (born February 1, 2004, in California) is a retired American Thoroughbred racehorse. He was sired by In Excess and out of the mare Truly Blessed. His damsire, French Depu ...

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 (Libor ) was an interest rate average calculated from estimates submitted by the leading Bank, banks in London. Each bank estimated what it would be charged were it to borrow from other banks. It was the prim ...

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 Fabio Mercurio (born 26 September 1966) is an Italian mathematician, internationally known for a number of results in mathematical finance. Main results Mercurio worked during his Ph.D. on incomplete markets theory using dynamic mean-variance hed ...

and Nicola Moreni.http://www.fabiomercurio.it/stochinf.pdf, Pricing Inflation Indexed options with stochastic volatility, Fabio Mercurio, Nicola Moreni, August 2005

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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

Derivative

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