# cfbyhw

Price cash flows from Hull-White interest-rate tree

## Description

example

[Price,PriceTree] = cfbyhw(HWTree,CFlowAmounts,CFlowDates,Settle) prices cash flows from a Hull-White interest-rate tree.

example

[Price,PriceTree] = cfbyhw(___,Basis,Options) adds optional arguments.

## Examples

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Price a portfolio containing two cash flow instruments paying interest annually over the four-year period from January 1, 2005 to January 1, 2009.

Load the file deriv.mat, which provides HWTree. The HWTree structure contains the time and interest-rate information needed to price the instruments.

The valuation date (settle date) specified in HWTree is January 1, 2004 (date number 731947).

HWTree.RateSpec.ValuationDate
ans =

731947

Provide values for the other required arguments.

CFlowAmounts =[5 NaN 5.5 105; 5 0 6 105];
CFlowDates = [731947 NaN 732678 733043;
731947 732313 732678 733043];

Use this information to compute the prices of the two cash flow instruments.

[Price, PriceTree] = cfbyhw(HWTree, CFlowAmounts, CFlowDates,...
HWTree.RateSpec.ValuationDate)
Price =

104.3334
104.8032

PriceTree =

struct with fields:

FinObj: 'HWPriceTree'
PTree: {[2×1 double]  [2×3 double]  [2×5 double]  [2×5 double]  [2×5 double]}
tObs: [0 1 2 3 4]
Connect: {[2]  [2 3 4]  [2 2 3 4 4]}
Probs: {[3×1 double]  [3×3 double]  [3×5 double]}

You can visualize the prices of the two cash flow instruments with the treeviewer function.

## Input Arguments

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Interest-rate tree structure, specified by using hwtree.

Data Types: struct

Cash flow amounts, specified as a Number of instruments (NINST) by maximum number of cash flows (MOSTCFS) matrix of cash flow amounts. Each row is a list of cash flow values for one instrument. If an instrument has fewer than MOSTCFS cash flows, the end of the row is padded with NaNs.

Data Types: double

Cash flow dates, specified as NINST-by-MOSTCFS vector using serial date numbers. Each entry contains the serial date number of the corresponding cash flow in CFlowAmounts.

Data Types: double

Settlement date, specified as a vector using serial date numbers or date character vectors. The Settle date for every cash flow is set to the ValuationDate of the HW tree. The cash flow argument, Settle, is ignored.

Data Types: double | char

(Optional) Day-count basis of the instrument, specified as a vector of integers.

• 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

Data Types: double

(Optional) Derivatives pricing options structure, specified using derivset.

Data Types: struct

## Output Arguments

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Expected prices at time 0, returned as a NINST-by-1 vector.

Tree structure of instrument prices, returned as a MATLAB® structure of trees containing vectors of instrument prices and observation times for each node. Within PriceTree:

• PriceTree.PTree contains the clean prices.

• PriceTree.tObs contains the observation times.

• PriceTree.Connect contains the connectivity vectors. Each element in the cell array describes how nodes in that level connect to the next. For a given tree level, there are NumNodes elements in the vector, and they contain the index of the node at the next level that the middle branch connects to. Subtracting 1 from that value indicates where the up-branch connects to, and adding 1 indicated where the down branch connects to.

• PriceTree.Probs contains the probability arrays. Each element of the cell array contains the up, middle, and down transition probabilities for each node of the level.

## Version History

Introduced before R2006a