crrsens

Instrument prices and sensitivities from Cox-Ross-Rubinstein tree

Syntax

[Delta, Gamma, Vega, Price] = crrsens(CRRTree, InstSet,
Options)

Arguments

CRRTree

Interest-rate tree structure created by crrtree.

InstSet

Variable containing a collection of NINST instruments. Instruments are categorized by type; each type can have different data fields. The stored data field is a row vector or string for each instrument.

Options

(Optional) Derivatives pricing options structure created with derivset.

Description

[Delta, Gamma, Vega, Price] = crrsens(CRRTree, InstSet,
Options)
computes dollar sensitivities and prices for instruments using a binomial tree created with crrtree. NINST instruments from a financial instrument variable, InstSet, are priced. crrsens handles instrument types: 'Asian', 'Barrier', 'Compound', 'Lookback', 'OptStock'. See instadd for information on instrument types.

Delta is an NINST-by-1 vector of deltas, representing the rate of change of instrument prices with respect to changes in the stock price. Delta is computed by finite differences in calls to crrtree. See crrtree for information on the stock tree.

Gamma is an NINST-by-1 vector of gammas, representing the rate of change of instrument deltas with respect to the changes in the stock price. Gamma is computed by finite differences in calls to crrtree.

Vega is an NINST-by-1 vector of vegas, representing the rate of change of instrument prices with respect to the changes in the volatility of the stock. Vega is computed by finite differences in calls to crrtree.

    Note   All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, divide by the respective instrument price.

Examples

expand all

Compute Sensitivities for Barrier and Lookback Instruments Using a crrtree

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

load deriv.mat;
CRRSubSet = instselect(CRRInstSet,'Type', ...
{'Barrier', 'Lookback'});

instdisp(CRRSubSet)
Index Type    OptSpec Strike Settle         ExerciseDates  AmericanOpt BarrierSpec Barrier Rebate Name     Quantity
1     Barrier call    105    01-Jan-2003    01-Jan-2006    1           ui          102     0      Barrier1 1       
 
Index Type     OptSpec Strike Settle         ExerciseDates  AmericanOpt Name      Quantity
2     Lookback call    115    01-Jan-2003    01-Jan-2006    0           Lookback1 7       
3     Lookback call    115    01-Jan-2003    01-Jan-2007    0           Lookback2 9       
 

Obtain the Delta and Gamma for the barrier and lookback options contained in the instrument set.

[Delta, Gamma] = crrsens(CRRTree, CRRSubSet)
Delta =

    0.6885
    0.6049
    0.8187


Gamma =

    0.0310
   -0.0000
         0

See Also

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