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Instrument sensitivities and prices using implied trinomial tree (ITT)
[Delta, Gamma, Vega] = ittsens(ITTTree,
InstSet)
[Delta, Gamma, Vega, Price] = ittsens(ITTTree,
InstSet)
[Delta, Gamma, Vega, Price] = ittsens(ITTTree,
InstSet,
Options)
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. |
[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.
Chriss, Neil. and I. Kawaller, Black-Scholes and Beyond: Options Pricing Models, McGraw-Hill, 1996, pp. 308-312.