Documentation

# 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.

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

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