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)``` to calculate instrument sensitivities and prices using an implied trinomial tree (ITT).

```[Delta, Gamma, Vega, Price] = ittsens(ITTTree, InstSet)``` to calculate a collection of instrument sensitivities and prices using an implied trinomial tree (ITT).

```[Delta, Gamma, Vega, Price] = ittsens(ITTTree, InstSet,Options)``` to calculate the sensitivities and prices for a collection of instruments that contain derivative pricing options using an implied trinomial tree (ITT).

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

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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.