itttree

Build implied trinomial stock tree

Syntax

ITTTree = itttree(StockSpec,RateSpec,TimeSpec,StockOptSpec)

Description

ITTTree = itttree(StockSpec,RateSpec,TimeSpec,StockOptSpec) builds an implied trinomial (ITT) stock tree.

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

StockSpec — Stock specification

structure

Stock specification, specified by the StockSpec obtained from stockspec. See stockspec for information on creating a stock specification.

Data Types: struct

RateSpec — Interest-rate specification for initial risk-free rate curve

structure

Interest-rate specification for initial risk-free rate curve, specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

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.