# ittprice

Price instruments using implied trinomial tree (ITT)

## Description

example

[Price,PriceTree] = ittprice(ITTTree,InstSet) price instruments using an implied trinomial tree (ITT) created with itttree. All instruments contained in a financial instrument variable, InstSet, are priced.

ittprice handles the following instrument types: optstock, barrier, Asian, lookback, and compound. Use instadd to construct the defined types.

example

[Price,PriceTree] = ittprice(___,Options) adds an optional input argument for Options.

## Examples

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Load the ITT tree and instruments from the data file deriv.mat.

Display the barrier and Asian options contained in the instrument set.

ITTSubSet = instselect(ITTInstSet,'Type', {'Barrier', 'Asian'});

instdisp(ITTSubSet)
Index Type    OptSpec Strike Settle         ExerciseDates  AmericanOpt BarrierSpec Barrier Rebate Name     Quantity
1     Barrier call    85     01-Jan-2006    31-Dec-2008    1           ui          115     0      Barrier1 1

Index Type  OptSpec Strike Settle         ExerciseDates  AmericanOpt AvgType    AvgPrice AvgDate Name   Quantity
2     Asian call    55     01-Jan-2006    01-Jan-2008    0           arithmetic NaN      NaN     Asian1 5
3     Asian call    55     01-Jan-2006    01-Jan-2010    0           arithmetic NaN      NaN     Asian2 7

Price the barrier and Asian options contained in the instrument set.

[Price, PriceTree] = ittprice(ITTTree, ITTSubSet)
Price = 3×1

2.4074
3.2052
6.6074

PriceTree = struct with fields:
FinObj: 'TrinPriceTree'
PTree: {[3x1 double]  [3x3 double]  [3x5 double]  [3x7 double]  [3x9 double]}
tObs: [0 1 2 3 4]
dObs: [732678 733043 733408 733773 734139]

## Input Arguments

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Implied trinomial stock tree structure, specified by using itttree.

Data Types: struct

Instrument variable containing a collection of NINST instruments, specified using instadd. Instruments are categorized by type; each type can have different data fields. The stored data field is a row vector or character vector for each instrument.

Data Types: struct

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

Data Types: struct

## Output Arguments

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Price for each instrument, returned as a NINST-by-1 vector. The prices are computed by backward dynamic programming on the stock tree. If an instrument cannot be priced, a NaN is returned in that entry.

For information on single-type pricing functions to retrieve state-by-state pricing tree information, see the following:

• barrierbyitt for pricing barrier options using an ITT tree

• optstockbyitt for pricing American, European, or Bermuda options using an ITT tree

• asianbyitt for pricing Asian options using an ITT tree

• lookbackbyitt for pricing lookback options using an ITT tree

• compoundbyitt for price compound options using an ITT tree

• cbondbyitt for pricing convertible bonds using an ITT tree

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

• PriceTree.PTree contains the clean prices.

• PriceTree.tObs contains the observation times.

• PriceTree.dObs contains the observation dates.

## Version History

Introduced in R2007a