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`InflationBond`

instrument object

Create and price an `InflationBond`

instrument object using
this workflow:

Use

`fininstrument`

to create an`InflationBond`

instrument object.Use

`ratecurve`

to specify an interest-rate model for the`InflationBond`

instrument.Use

`inflationcurve`

to specify an inflation curve model.Use

`finpricer`

to specify an`Inflation`

pricing method for the`InflationBond`

instrument.Use

`inflationCashflows`

to compute cash flows for the`InflationBond`

instrument.

For more detailed information on this workflow, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

For more information on the available models and pricing methods for an
`InflationBond`

instrument, see Choose Instruments, Models, and Pricers.

creates an `InflationBond`

= fininstrument(`InstrumentType`

,'`CouponRate`

',couponrate_value,'`Maturity`

',maturity_date)`InflationBond`

object by specifying
`InstrumentType`

and sets the properties for
the required name-value pair arguments `CouponRate`

and
`Maturity`

.

sets optional properties using
additional name-value pairs in addition to the required arguments in the
previous syntax. For example, `InflationBond`

= fininstrument(___,`Name,Value`

)```
InflationBond =
fininstrument("InflationBond",'Maturity',Maturity,'CouponRate',CouponRate,'IssueDate',IssueDate)
```

creates a `InflationBond`

option.

`inflationCashflows` | Compute cash flows for `InflationBond` instrument |

To price an inflation-indexed bond, use an inflation curve and a nominal discount curve (model-free approach), where the cash flows are discounted using the nominal discount curve.

$$\begin{array}{l}I(0,T){P}_{n}(0,T)=I(0){P}_{r}(0,T)\\ {B}_{TIPS}(0,{T}_{M})=\frac{1}{I({T}_{0})}{\displaystyle \sum _{i=1}^{M}cI(0){P}_{r}(0,{T}_{i})+FI(0){P}_{r}(0,{T}_{M})}\\ \text{}=\frac{1}{I({T}_{0})}{\displaystyle \sum _{i=1}^{M}cI(0,{T}_{i}){P}_{n}(0,{T}_{i})+FI(0,{T}_{M})}{P}_{n}(0,{T}_{M})\end{array}$$

where

*P*_{n}is the nominal zero-coupon bond price.*P*_{r}is the real zero-coupon bond price.*k*is the fixed inflation rate.*I*(0,*T*) is the breakeven inflation index for period (0,*T*).*I*(0) is the inflation index at (*t*= 0).*I*(*T*_{0}) is the base inflation index at the issue date (t =*T*_{0}).*B*_{TIPS}(0,*T*_{M}) is the inflation-indexed bond price.*I*(*T*_{i-1}) is the inflation index at the start date with some lag (for example, three months).*C*is the coupon.*F*is the face value.

[1] Brody, D. C., Crosby, J., and
Li, H. "Convexity Adjustments in Inflation-Linked Derivatives." *Risk
Magazine*. November 2008, pp. 124–129.

[2] Kerkhof, J. "Inflation
Derivatives Explained: Markets, Products, and Pricing." *Fixed Income
Quantitative Research*, Lehman Brothers, July 2005.

[3] Zhang, J. X. "Limited Price
Indexation (LPI) Swap Valuation Ideas." *Wilmott Magazine*. no. 57,
January 2012, pp. 58–69.