Financial Derivatives Toolbox™

bkprice

Instrument prices from Black-Karasinski interest-rate tree

Syntax

[Price, PriceTree] = bkprice(BKTree, InstSet, Options)

Arguments

`BKTree`	Interest-rate tree structure created by `bktree`.
`InstSet`	Variable containing a collection of `NINST` 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, PriceTree] = bkprice(BKTree, InstSet, Options) computes arbitrage-free prices for instruments using an interest-rate tree created with bktree. All instruments contained in a financial instrument variable, InstSet, are priced.

Price is a number of instruments (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.PTree contains the clean prices.

PriceTree.AITree contains the accrued interest.

PriceTree.tObs contains the observation times.

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

Related single-type pricing functions are

bondbybk: Price a bond from a Black-Karasinski tree.
capbybk: Price a cap from a Black-Karasinski tree.
cfbybk: Price an arbitrary set of cash flows from a Black-Karasinski tree.
fixedbybk: Price a fixed-rate note from a Black-Karasinski tree.
floatbybk: Price a floating-rate note from a Black-Karasinski tree.
floorbybk: Price a floor from a Black-Karasinski tree.
optbndbybk: Price a bond option from a Black-Karasinski tree.
optembndbybk: Price a bond with embedded option by a Black-Karasinski tree.
swapbybk: Price a swap from a Black-Karasinski tree.
swaptionbybk: Price a swaption from a Black-Karasinski tree.

Examples

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

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

instdisp(BKSubSet)

Index Type   CouponRate Settle      Maturity    Period  Name ... 
1     Bond   0.03       01-Jan-2004 01-Jan-2007 1       3% bond
2     Bond   0.03       01-Jan-2004 01-Jan-2008 2       3% bond
     
Index Type Strike Settle      Maturity     CapReset...  Name ...  
3     Cap  0.04   01-Jan-2004 01-Jan-2008  1            4% Cap 
     
[Price, PriceTree] = bkprice(BKTree, BKSubSet);

Price =

   98.1096
   95.6734
    2.2706

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

treeviewer(PriceTree, BKSubSet)

bkprice

Syntax

Arguments

Description

Examples

See Also