Build inflation curve from market zero-coupon inflation swap rates
specifies options using one or more name-value pair arguments in addition to any of the
input argument combinations in the previous syntax. For example,
myInflationCurve = inflationbuild(___,
inflationcurve object from market zero ZCIS dates and rates.
Build Inflation Curve from Zero-Coupon Inflation Swap Rates
Define the inflation curve parameters.
BaseDate = datetime(2020,9,20); BaseIndexValue = 100; ZCISTimes = [calyears([1 2 3 4 5 7 10 20 30])]'; ZCISRates = [0.51 0.65 0.87 0.92 0.95 1.42 1.75 2.03 2.54]'./100; ZCISDates = BaseDate + ZCISTimes; SeasonalRates = [-0.19 -0.09 -0.04 0.1 0.16 0.11 0.26 0.17 -0.07 -0.08 -0.14 -0.19]'./100;
myInflationCurve = inflationbuild(BaseDate,BaseIndexValue,ZCISDates,ZCISRates,'Seasonality',SeasonalRates)
myInflationCurve = inflationcurve with properties: Basis: 0 Dates: [10x1 datetime] InflationIndexValues: [10x1 double] ForwardInflationRates: [9x1 double] Seasonality: [12x1 double]
BaseDate — Base date of inflation curve
datetime | serial date number | date character vector | date string
Base date of inflation curve, specified as a scalar datetime, serial date number, date character vector, or date string.
BaseIndexValue — Base index value of inflation curve
Base index value of inflation curve, specified as a scalar numeric.
ZCISDates — Market ZCIS maturity dates minus lag
datetimes | serial date numbers | cell array of date character vectors | date strings
Market ZCIS maturity dates minus lag, specified as an
1 vector of datetimes, serial date
numbers, cell array of date character vectors, or date string array.
ZCISRates — Market ZCIS rates
Market ZCIS rates, specified as an
vector of decimals.
Specify optional pairs of arguments as
the argument name and
Value is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name in quotes.
Basis — Day count basis
0 (actual/actual) (default) | integer from
Day count basis, specified as the comma-separated pair consisting of
'Basis' and a scalar integer.
0 — actual/actual
1 — 30/360 (SIA)
2 — actual/360
3 — actual/365
4 — 30/360 (PSA)
5 — 30/360 (ISDA)
6 — 30/360 (European)
7 — actual/365 (Japanese)
8 — actual/actual (ICMA)
9 — actual/360 (ICMA)
10 — actual/365 (ICMA)
11 — 30/360E (ICMA)
12 — actual/365 (ISDA)
13 — BUS/252
For more information, see Basis.
Seasonality — Seasonal adjustment rates
1 vector of
0s (no seasonality) (default) | decimal
Seasonal adjustment rates, specified as the comma-separated pair consisting of
'Seasonality' and a
vector in decimals for each month ordered from January to December. The rates are
annualized and continuously compounded seasonal rates that are internally corrected to
FirstMonthIndex — First month inflation index
 (not known) (default) | positive numeric
First month inflation index, specified as the comma-separated pair consisting of
'FirstMonthIndex' and a positive numeric.
Build an inflation curve from a series of breakeven zero-coupon inflation swap (ZCIS) rates:
is the breakeven inflation index reference number for maturity date Ti.
is the base inflation index value for the starting date T0.
is the breakeven inflation rate for the ZCIS maturing on Ti.
The ZCIS rates typically have maturities that increase in whole number of years, so the inflation curve is built on an annual basis. From the annual basis inflation curve, the annual unadjusted (that is, not seasonally adjusted) forward inflation rates are computed as follows:
The unadjusted forward inflation rates are used for interpolating and also for incorporating seasonality to the inflation curve.
For monthly periods that are not a whole number of years, seasonal adjustments can be made to reflect seasonal patterns of inflation within the year. These 12 monthly seasonal adjustments are annualized and they add up to zero to ensure that the cumulative seasonal adjustments are reset to zero every year.
is the breakeven inflation index reference number.
is the previous inflation reference number.
fi is the annual unadjusted forward inflation rate.
si is the annualized seasonal component for the period .
The first year seasonal adjustment may need special treatment because, typically, the breakeven inflation reference number of the first month is already known. If that is the case, the unadjusted forward inflation rate for the first year needs to be recomputed for the remaining 11 months.