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ittsens

Instrument sensitivities and prices using implied trinomial tree (ITT)

Syntax

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

Description

example

[Delta,Gamma,Vega,Price] = ittsens(ITTTree,InstSet) calculates instrument sensitivities and prices using an implied trinomial tree (ITT) that is created with the itttree function. All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, divide by the respective instrument price.

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

example

[Delta,Gamma,Vega,Price] = ittsens(___,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 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.<br>This made extrapolation necessary. Below is a list of the options that were outside of the<br>range of those specified in StockOptSpec.<br><br>Option Type: 'call'   Maturity: 01-Jan-2007  Strike=67.2897<br>Option Type: 'put'   Maturity: 01-Jan-2007  Strike=37.1528<br>Option Type: 'put'   Maturity: 01-Jan-2008  Strike=27.6066<br>Option Type: 'put'   Maturity: 31-Dec-2008  Strike=20.5132<br>Option Type: 'call'   Maturity: 01-Jan-2010  Strike=164.0157<br>Option Type: 'put'   Maturity: 01-Jan-2010  Strike=15.2424<br>
Delta = 3×1

    0.2387
   -0.4283
    0.3482

Gamma = 3×1

    0.0260
    0.0188
    0.0380

Input Arguments

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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

Derivatives pricing options structure, created using derivset.

Data Types: struct

Output Arguments

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Rate of change of instruments prices with respect to changes in the stock price, returned as a NINST-by-1 vector of deltas.

For path-dependent options ('Lookback' and 'Asian'), Delta and Gamma are computed by finite differences in calls to ittprice. For the rest of the options ('OptStock', 'Barrier', 'CBond', and 'Compound'), Delta and Gamma are computed from the ITTTree and the corresponding option price tree.

Rate of change of instruments deltas with respect to changes in the stock price, returned as a NINST-by-1 vector of gammas.

For path-dependent options ('Lookback' and 'Asian'), Delta and Gamma are computed by finite differences in calls to ittprice. For the rest of the options ('OptStock', 'Barrier', 'CBond', and 'Compound'), Delta and Gamma are computed from the ITTTree and the corresponding option price tree.

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

Price of 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.

References

[1] Chriss, Neil. Black-Scholes and Beyond: Option Pricing Models. McGraw-Hill, 1996, pp 308-312.

Introduced in R2007a