itttree
Build implied trinomial stock tree
Description
Examples
Create an ITT Tree
Assume that the interest rate is fixed at 8% annually between the valuation date of the tree (January 1, 2006) until its maturity.
Rate = 0.08; ValuationDate = '01-01-2006'; EndDate = '01-01-2008'; RateSpec = intenvset('StartDates', ValuationDate, 'EndDates', EndDate, ... 'ValuationDate', ValuationDate, 'Rates', Rate, 'Compounding', -1);
To build an ITTTree
, create the StockSpec
, TimeSpec
,
and StockOptSpec
structures.
Sigma = 0.20; AssetPrice = 50; DividendType = 'cash'; DividendAmounts = [0.50; 0.50; 0.50; 0.50]; ExDividendDates = {'03-Jan-2007'; '01-Apr-2007'; '05-July-2007';'01-Oct-2007'} StockSpec = stockspec(Sigma, AssetPrice, DividendType, ... DividendAmounts, ExDividendDates); ValuationDate = '01-01-2006'; EndDate = '01-01-2008'; NumPeriods = 4; TimeSpec = itttimespec(ValuationDate, EndDate, NumPeriods);
Build a StockOptSpec
structure.
Settle = '01/01/06'; Maturity = ['07/01/06'; '07/01/06'; '07/01/06'; '07/01/06'; '01/01/07'; '01/01/07'; '01/01/07'; '01/01/07'; '07/01/07'; '07/01/07'; '07/01/07'; '07/01/07'; '01/01/08'; '01/01/08'; '01/01/08'; '01/01/08']; Strike = [113; 101; 100; 88; 128; 112; 100; 78; 144; 112; 100; 69; 162; 112; 100; 61]; OptPrice =[ 0; 4.807905472659144; 1.306321897011867; 0.048039195057173; 0; 2.310953054191461; 1.421950392866235; 0.020414826276740; 0; 5.091986935627730; 1.346534812295291; 0.005101325584140; 0; 8.047628153217246; 1.219653432150932; 0.001041436654748]; OptSpec = { 'call'; 'call'; 'put'; 'put'; 'call'; 'call'; 'put'; 'put'; 'call'; 'call'; 'put'; 'put'; 'call'; 'call'; 'put'; 'put'}; StockOptSpec = stockoptspec(OptPrice, Strike, Settle, Maturity, OptSpec);
Use itttree
to build the ITTTree
structure.
Note, in this example, the extrapolation warnings are turned on. These
warnings are a consequence of having to extrapolate to find the option
price of the tree nodes. In this example, the set of inputs options
was too narrow for the shift in the tree nodes introduced by the disturbance
used to calculate the sensitivities. As a consequence extrapolation
for some of the nodes was needed.
warning('on', 'fininst:itttree:Extrapolation'); ITTTree = itttree(StockSpec, RateSpec, TimeSpec, StockOptSpec)
Warning: The option set specified in StockOptSpec was too narrow for the generated tree. This made extrapolation necessary. Below is a list of the options that were outside of the range of those specified in StockOptSpec. Option Type: 'call' Maturity: 02-Jul-2006 Strike=60.7466 Option Type: 'put' Maturity: 02-Jul-2006 Strike=50.0731 Option Type: 'put' Maturity: 02-Jul-2006 Strike=41.3344 Option Type: 'call' Maturity: 01-Jan-2007 Strike=73.8592 Option Type: 'call' Maturity: 01-Jan-2007 Strike=60.8227 Option Type: 'put' Maturity: 01-Jan-2007 Strike=50.1492 Option Type: 'put' Maturity: 01-Jan-2007 Strike=41.4105 Option Type: 'put' Maturity: 01-Jan-2007 Strike=34.2559 Option Type: 'call' Maturity: 02-Jul-2007 Strike=88.8310 Option Type: 'call' Maturity: 02-Jul-2007 Strike=72.9081 Option Type: 'call' Maturity: 02-Jul-2007 Strike=59.8715 Option Type: 'put' Maturity: 02-Jul-2007 Strike=49.1980 Option Type: 'put' Maturity: 02-Jul-2007 Strike=40.4594 Option Type: 'put' Maturity: 02-Jul-2007 Strike=33.3047 Option Type: 'put' Maturity: 02-Jul-2007 Strike=27.4470 Option Type: 'call' Maturity: 01-Jan-2008 Strike=107.2895 Option Type: 'call' Maturity: 01-Jan-2008 Strike=87.8412 Option Type: 'call' Maturity: 01-Jan-2008 Strike=71.9183 Option Type: 'call' Maturity: 01-Jan-2008 Strike=58.8817 Option Type: 'put' Maturity: 01-Jan-2008 Strike=48.2083 Option Type: 'put' Maturity: 01-Jan-2008 Strike=39.4696 Option Type: 'put' Maturity: 01-Jan-2008 Strike=32.3150 Option Type: 'put' Maturity: 01-Jan-2008 Strike=26.4573 Option Type: 'put' Maturity: 01-Jan-2008 Strike=21.6614 > In itttree>InterpOptPrices at 675 In itttree at 277 ITTTree = FinObj: 'ITStockTree' StockSpec: [1x1 struct] StockOptSpec: [1x1 struct] TimeSpec: [1x1 struct] RateSpec: [1x1 struct] tObs: [0 0.500000000000000 1 1.500000000000000 2] dObs: [732678 732860 733043 733225 733408] STree: {1x5 cell} Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double]}
Input Arguments
TimeSpec
— Tree time layout specification
structure
Tree time layout specification, specified by the TimeSpec
obtained
from itttimespec
. The TimeSpec
defines
the observation dates of the ITT tree. See itttimespec
for
information on the tree structure.
Data Types: struct
StockOptSpec
— Option stock specification
structure
Option stock specification, specified by the StockOptSpec
obtained
from stockoptspec
. See stockoptspec
for information on creating
a stock specification.
Data Types: struct
Output Arguments
ITTTree
— ITT trinomial tree
structure
ITT trinomial tree, returned as a structure specifying the time layout for the tree.
Version History
Introduced in R2007a
See Also
intenvset
| ittprice
| stockspec
| itttimespec
| stockoptspec
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