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ittsens

Instrument sensitivities and prices using implied trinomial tree (ITT)

Syntax

[Delta, Gamma, Vega] = ittsens(ITTTree, InstSet)
[Delta, Gamma, Vega, Price] = ittsens(ITTTree, InstSet)
[Delta, Gamma, Vega, Price] = ittsens(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

[Delta, Gamma, Vega] = ittsens(ITTTree, InstSet)

[Delta, Gamma, Vega, Price] = ittsens(ITTTree, InstSet)

[Delta, Gamma, Vega, Price] = ittsens(ITTTree, InstSet,
Options)

The outputs for ittsens are:

  • Delta is a NINST-by-1 vector of deltas, representing the rate of change of instruments prices with respect to changes in the stock price.

  • Gamma is a NINST-by-1 vector of gammas, representing the rate of change of instruments deltas with respect to changes in the stock price.

  • Vega is a NINST-by-1 vector of vegas, representing the rate of change of instruments prices with respect to changes in the volatility of the stock. Vega is computed by finite differences in calls to itttree.

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

ittsens computes dollar sensitivities and prices for instruments using an ITT tree created with itttree.

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

For path-dependent options (lookbacks and Asians), Delta and Gamma are computed by finite differences in calls to ittprice. For the rest of the options (optstock, barrier, and compound), Delta and Gamma are computed from the ITT tree and the corresponding option price tree.

All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, they must be divided by their respective instrument price.

Examples

expand all

Compute Instrument Sensitivities Using an Implied Trinomial Tree (ITT)

Load the ITT tree and instruments from the data file deriv.mat and display the vanilla options and barrier option instruments.

load deriv.mat
ITTSubSet = instselect(ITTInstSet,'Type', {'OptStock', 'Barrier'});

instdisp(ITTSubSet)
Index Type     OptSpec Strike Settle         ExerciseDates  AmericanOpt Name  Quantity
1     OptStock call    95     01-Jan-2006    31-Dec-2008    1           Call1 10      
2     OptStock put     80     01-Jan-2006    01-Jan-2010    0           Put1   4      
 
Index Type    OptSpec Strike Settle         ExerciseDates  AmericanOpt BarrierSpec Barrier Rebate Name     Quantity
3     Barrier call    85     01-Jan-2006    31-Dec-2008    1           ui          115     0      Barrier1 1       
 

Compute the Delta and Gamma sensitivities of vanilla options and barrier option contained in the instrument set.

[Delta, Gamma] = ittsens(ITTTree, ITTSubSet)
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: 01-Jan-2007  Strike=67.2897
Option Type: 'put'   Maturity: 01-Jan-2007  Strike=37.1528
Option Type: 'put'   Maturity: 01-Jan-2008  Strike=27.6066
Option Type: 'put'   Maturity: 31-Dec-2008  Strike=20.5132
Option Type: 'call'   Maturity: 01-Jan-2010  Strike=164.0157
Option Type: 'put'   Maturity: 01-Jan-2010  Strike=15.2424
 

Delta =

    0.2387
   -0.4283
    0.3482


Gamma =

    0.0260
    0.0188
    0.0380

References

Chriss, Neil. and I. Kawaller, Black-Scholes and Beyond: Options Pricing Models, McGraw-Hill, 1996, pp. 308-312.

See Also

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