hjmprice (Financial Derivatives Toolbox)

Fixed income instrument prices by HJM interest rate tree

Syntax

[Price, PriceTree] = hjmprice(HJMTree, InstSet, Options)

Arguments

HJMTree
Heath-Jarrow-Morton tree sampling a forward rate process. See hjmtree for information on creating HJMTree.

InstSet
Variable containing a collection of instruments. Instruments are categorized by type; each type can have different data fields. The stored data field is a row vector or string for each instrument.

Options
(Optional) Derivatives pricing options structure created with derivset.

`HJMTree`	Heath-Jarrow-Morton tree sampling a forward rate process. See `hjmtree` for information on creating `HJMTree`.
`InstSet`	Variable containing a collection of instruments. Instruments are categorized by type; each type can have different data fields. The stored data field is a row vector or string for each instrument.
Options	(Optional) Derivatives pricing options structure created with `derivset`.

Description

Price = hjmprice(HJMTree, InstSet, Options) computes arbitrage free prices for instruments using an interest rate tree created with hjmtree. NINST instruments from a financial instrument variable, InstSet, are priced.

Price is a NINST-by-1 vector of prices for each instrument. The prices are computed by backward dynamic programming on the interest rate tree. If an instrument cannot be priced, NaN is returned.

PriceTree is a MATLAB structure of trees containing vectors of instrument prices and accrued interest, and a vector of observation times for each node.

PriceTree.PBush contains the clean prices.

PriceTree.AIBush contains the accrued interest.

PriceTree.tObs contains the observation times.

hjmprice handles instrument types: 'Bond', 'CashFlow', 'OptBond', 'Fixed', 'Float', 'Cap', 'Floor', 'Swap'. See instadd to construct defined types.

Related single-type pricing functions are:

bondbyhjm: Price a bond by an HJM tree.
capbyhjm: Price a cap by an HJM tree.
cfbyhjm: Price an arbitrary set of cash flows by an HJM tree.
fixedbyhjm: Price a fixed rate note by an HJM tree.
floatbyhjm: Price a floating rate note by an HJM tree.
floorbyhjm: Price a floor by an HJM tree.
optbndbyhjm: Price a bond option by an HJM tree.
swapbyhjm: Price a swap by an HJM tree.

Examples

Load the HJM tree and instruments from the data file deriv.mat. Price the cap and bond instruments contained in the instrument set.

load deriv.mat; 
HJMSubSet = instselect(HJMInstSet,'Type', {'Bond', 'Cap'}); 

instdisp(HJMSubSet)

Index  Type  CouponRate Settle      Maturity     Period  Name ... 
1      Bond  0.04       01-Jan-2000 01-Jan-2003  1       4% bond   
2      Bond  0.04       01-Jan-2000 01-Jan-2004  2       4% bond   
 
Index Type Strike Settle      Maturity     CapReset...  Name ...  
3     Cap  0.03   01-Jan-2000 01-Jan-2004  1            3% Cap 
     
[Price, PriceTree] = hjmprice(HJMTree, HJMSubSet)

Warning: Not all cash flows are aligned with the tree. Result will 
be approximated.

Price =

   98.7159
   97.5280
    6.2831
PriceTree = 

    FinObj: 'HJMPriceTree'
     PBush: {1x5 cell}
    AIBush: {1x5 cell}
      tObs: [0 1 2 3 4]

You can use treeviewer to see the prices of these three instruments along the price tree.

```
treeviewer(PriceTree, HJMSubSet)
```

hedgeslf hjmsens