hwtree
Build Hull-White interest-rate tree
Description
Examples
Create an HWTree
Using the data provided, create a Hull-White volatility specification (VolSpec
), rate specification (RateSpec
), and tree time layout specification (TimeSpec
). Then, use these specifications to create a Hull-White tree using hwtree
.
Compounding = -1; ValuationDate = '01-01-2004'; StartDate = ValuationDate; VolDates = ['12-31-2004'; '12-31-2005'; '12-31-2006'; '12-31-2007']; VolCurve = 0.01; AlphaDates = '01-01-2008'; AlphaCurve = 0.1; Rates = [0.0275; 0.0312; 0.0363; 0.0415]; HWVolSpec = hwvolspec(ValuationDate, VolDates, VolCurve,... AlphaDates, AlphaCurve); RateSpec = intenvset('Compounding', Compounding,... 'ValuationDate', ValuationDate,... 'StartDates', ValuationDate,... 'EndDates', VolDates,... 'Rates', Rates); HWTimeSpec = hwtimespec(ValuationDate, VolDates, Compounding); HWTree = hwtree(HWVolSpec, RateSpec, HWTimeSpec)
HWTree = struct with fields:
FinObj: 'HWFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 0.9973 1.9973 2.9973]
dObs: [731947 732312 732677 733042]
CFlowT: {[4x1 double] [3x1 double] [2x1 double] [3.9973]}
Probs: {[3x1 double] [3x3 double] [3x5 double]}
Connect: {[2] [2 3 4] [2 3 4 5 6]}
FwdTree: {[1.0278] [1.0536 1.0356 1.0178] [1.0847 1.0661 1.0478 1.0298 1.0121] [1.1156 1.0965 1.0776 1.0591 1.0409 1.0231 1.0055]}
Use treeviewer
to observe the tree you have created.
Input Arguments
TimeSpec
— Time layout specification
structure
Time layout specification, specified using the TimeSpec
obtained
from hwtimespec
. The TimeSpec
defines
the observation dates of the HW tree and the compounding rule for
date to time mapping and price-yield formulas. See hwtimespec
for information on the tree
structure.
Data Types: struct
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: HWTree = hwtree(VolSpec,RateSpec,TimeSpec,'Method','HW1996')
Method
— Hull-White method upon which tree-node connectivity algorithm is based
HW2000
(default) | character vector with values of HW1996
or HW2000
Hull-White method upon which the tree-node connectivity algorithm
is based, specified a character vector with a value of HW1996
or HW2000
.
Note
hwtree
supports two tree-node connectivity
algorithms. HW1996
is based on the original paper
published in the Journal of Derivatives, and HW2000
is
the general version of the algorithm, as specified in the paper published
in August 2000.
Data Types: char
Output Arguments
HWTree
— Hull-White interest-rate tree
structure
Hull-White interest-rate tree, returned as a structure containing time and interest rate information of a trinomial recombining tree.
The HWTree
structure returned contains all
the information necessary to propagate back any cash flows occurring
during the time span of the tree. The main fields of HWTree
are:
HWTree.tObs
contains the time factor of each level of the tree.HWTree.dObs
contains the date of each level of the tree.HWTree.Probs
contains a cell array of3
-by-N
numeric arrays with the up/mid/down probabilities of each node of the tree except for the last level. The cells in the cell array are ordered from root node. The arrays are3
-by-N
with the first row corresponding to an up-move, the mid row to a mid-move and so on. Each column of the array represents a node starting from the top node of a given level.HWTree.Connect
contains a cell array with connectivity information for each node of the tree. The arrangement is similar toHWTree.Probs
, with the exception that it has only one row in each cell. The number represents the node in the next level to which the middle branch connects to. The top branch connects to the value above (minus one) and the lower branch connects to the value below (plus one).HWTree.FwdTree
contains the forward spot rate from one node to the next. The forward spot rate is defined as the inverse of the discount factor.
References
[1] Hull, J., and A. White. "Using Hull-White Interest Rate Trees." Journal of Derivatives. 1996.
[2] Hull, J., and A. White. "The General Hull-White Model and Super Calibration.” August 2000.
Version History
Introduced before R2006a
See Also
hwcalbycap
| hwcalbyfloor
| hwprice
| hwtimespec
| hwvolspec
| intenvset
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