Financial Derivatives Toolbox™

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

Load the ITT tree and instruments from the data file deriv.mat. Compute the Delta and Gamma sensitivities of vanilla options and barrier option contained in the instrument set.

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

instdisp(ITTSubSet)
>> 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 ExercDates AmerOpt BarrSpec Barr Rebate Name Quantity
3   Barrier call    85   01-Jan-2006  31-Dec-2008    1     ui    115    0    Barrier1 1

[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

> In itttree>InterpOptPrices at 675
  In itttree at 277
  In stocktreesens>stocktreevega at 191
  In stocktreesens at 92
  In ittsens at 81

Delta =

    0.2387
   -0.4283
    0.3482

Gamma =

   0.0260
   0.0188
   0.0380

References