Financial Derivatives Toolbox™

hwprice - Instrument prices from Hull-White interest-rate tree

Syntax

[Price, PriceTree] = hwprice(HWTree, InstSet, Options)

Arguments

Description

[Price, PriceTree] = hwprice(HWTree, InstSet, Options) computes arbitrage-free prices for instruments using an interest-rate tree created with hwtree. 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.

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

Related single-type pricing functions are

• bondbyhw: Price a bond from a Hull-White tree.

• capbyhw: Price a cap from a Hull-White tree.

• cfbyhw: Price an arbitrary set of cash flows from a Hull-White tree.

• fixedbyhw: Price a fixed-rate note from a Hull-White tree.

• floatbyhw: Price a floating-rate note from a Hull-White tree.

• floorbyhw: Price a floor from a Hull-White tree.

• optbndbyhw: Price a bond option from a Hull-White tree.

• optembndbyhw: Price a bond with embedded option by a Hull-White tree.

• swapbyhw: Price a swap from a Hull-White tree.

• swaptionbyhw: Price a swaption from a Hull-White tree.

Examples

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

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

instdisp(HWSubSet)

Index Type   CouponRate Settle      Maturity    Period  Name ... 
1     Bond   0.04       01-Jan-2004 01-Jan-2007 1       4% bond
2     Bond   0.04       01-Jan-2004 01-Jan-2008 1       4% bond
     
Index Type Strike Settle      Maturity     CapReset...  Name ...  
3     Cap  0.06   01-Jan-2004 01-Jan-2008  1            6% Cap 
     
[Price, PriceTree] = hwprice(HWTree, HWSubSet);

Price =

  100.9188
   99.3296
    0.5837

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

treeviewer(PriceTree, HWSubSet)

See Also

hwsens, hwtree, instadd, intenvprice, intenvsens

hjmvolspec

hwsens