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ittprice

Price instruments using implied trinomial tree (ITT)

Syntax

Price = ittprice(ITTTree,InstSet)
Price = ittprice(ITTTree,InstSet,Options)
[Price,PriceTree] = ittprice(ITTTree,InstSet,Options)

Arguments

ITTTree

Implied trinomial stock tree. See itttree for information on creating the variable ITTTree.

InstSet

Variable containing a collection of NINST instruments. Instruments are broken down by type and each type can have different data fields.

Options

(Optional) Structure created using derivset containing derivative pricing options.

Description

Price = ittprice(ITTTree,InstSet) to price instruments using an implied trinomial tree (ITT).

Price = ittprice(ITTTree,InstSet,Options) to price instruments with derivative pricing options using an implied trinomial tree (ITT).

[Price,PriceTree] = ittprice(ITTTree,InstSet,Options) to price a collection of instruments with derivative pricing options using an implied trinomial tree (ITT).

The outputs for ittprice are:

  • Price is a NINST-by-1 vector of prices of each instrument at time 0. 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.

  • PriceTree is a structure containing trees of vectors of instrument prices and a vector of observation times for each node.

    • PriceTree.PTree contains the prices.

    • PriceTree.tObs contains the observation times.

    • PriceTree.dObs contains the observation dates.

ittprice computes prices for instruments using an implied trinomial tree created with itttree.

Note

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

When using an implied trinomial tree, pricing of path-dependent options is done using Hull-White. So, for these options there are no unique prices on the tree nodes except for the root node. The corresponding nodes of the tree are populated with NaNs for these particular options. 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

Examples

collapse all

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

load 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 = 

    2.4074
    3.2052
    6.6074

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

Introduced in R2007a

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