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eqpsens

Instrument prices and sensitivities from Equal Probabilities binomial tree

Syntax

[Delta,Gamma,Vega,Price] = eqpsens(EQPTree,InstSet)
[Delta,Gamma,Vega,Price] = eqpsens(___,Options)

Description

example

[Delta,Gamma,Vega,Price] = eqpsens(EQPTree,InstSet) computes instrument sensitivities and prices for instruments using a binomial tree created with the eqptree function. All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, divide by the respective instrument price.

eqpsens handles instrument types: 'Asian', 'Barrier', 'Compound', 'CBond', 'Lookback', and 'OptStock'. See instadd for information on instrument types.

example

[Delta,Gamma,Vega,Price] = eqpsens(___,Options) adds an optional input argument for Options.

Examples

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

load deriv.mat; 

EQPSubSet = instselect(EQPInstSet, 'FieldName', 'OptSpec', ...
'Data', 'put')
EQPSubSet = struct with fields:
        FinObj: 'Instruments'
    IndexTable: [1x1 struct]
          Type: {5x1 cell}
     FieldName: {5x1 cell}
    FieldClass: {5x1 cell}
     FieldData: {5x1 cell}

instdisp(EQPSubSet)
Index Type     OptSpec Strike Settle         ExerciseDates  AmericanOpt Name  Quantity
1     OptStock put     105    01-Jan-2003    01-Jan-2006    0           Put1   5      
 
Index Type  OptSpec Strike Settle         ExerciseDates  AmericanOpt AvgType    AvgPrice AvgDate Name   Quantity
2     Asian put     110    01-Jan-2003    01-Jan-2006    0           arithmetic NaN      NaN     Asian1 4       
3     Asian put     110    01-Jan-2003    01-Jan-2007    0           arithmetic NaN      NaN     Asian2 6       
 

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

[Delta, Gamma] = eqpsens(EQPTree, EQPSubSet)
Delta = 3×1

   -0.2336
   -0.5443
   -0.4516

Gamma = 3×1

    0.0218
    0.0000
    0.0000

Input Arguments

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Stock tree structure, specified by using eqptree.

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 eqpprice. For the rest of the options ('OptStock', 'Barrier', 'CBond', and 'Compound'), Delta and Gamma are computed from the EQPTree 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 eqpprice. For the rest of the options ('OptStock', 'Barrier', 'CBond', and 'Compound'), Delta and Gamma are computed from the EQPTree 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 eqptree.

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.

References

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

Introduced before R2006a