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basketstockspec

Specify basket stock structure using Longstaff-Schwartz model

Syntax

BasketStockSpec = basketstockspec(Sigma, AssetPrice, Quantity,
Correlation)
BasketStockSpec = basketstockspec(Sigma, AssetPrice, Quantity,
Correlation, 'ParameterName',ParameterValue ...)

Description

BasketStockSpec = basketstockspec(Sigma, AssetPrice, Quantity,
Correlation)
creates a basket stock structure.

BasketStockSpec = basketstockspec(Sigma, AssetPrice, Quantity,
Correlation, 'ParameterName',ParameterValue ...)
accepts optional inputs as one or more comma-separated parameter/value pairs. 'ParameterName' is the name of the parameter inside single quotes. 'ParameterValue is the value corresponding to 'ParameterName'. Specify parameter-value pairs in any order. Names are case-insensitive and partial string matches are allowable, if no ambiguities exist.

Input Arguments

Sigma

NINST-by-1 vector of decimal annual price volatility of the underlying security.

AssetPrice

NINST-by-1 vector of underlying asset price values at time 0.

Quantity

NINST-by-1 vector of quantities of the instruments contained in the basket.

Correlation

NINST-by-NINST matrix of correlation values.

Parameter–Value Pairs

DividendAmounts

NINST-by-1 cell array specifying the dividend amounts for basket instruments. Each element of the cell array is a 1-by-NDIV row vector of cash dividends or a scalar representing a continuous annualized dividend yield for the corresponding instrument.

DividendType

NINST-by-1 cell array of strings specifying each stock's dividend type. Dividend type must be either cash for actual dollar dividends or continuous for continuous dividend yield. .

ExDividendDates

NINST-by-1 cell array specifying the ex-dividend dates for the basket instruments. Each row is a 1-by-NDIV matrix of ex-dividend dates for cash type. For rows that correspond to basket instruments with continuous dividend type, the cell is empty. If none of the basket instruments pay continuous dividends, do not specify ExDividendDates.

Output Arguments

BasketStockSpec

Structure encapsulating the properties of a basket stock structure.

Examples

expand all

Create a Basket Stock Structure for Three Stocks

Find a basket option of three stocks. The stocks are currently trading at $56, $92 and $125 with annual volatilities of 20%, 12% and 15%, respectively. The basket option contains 25% of the first stock, 40% of the second stock, and 35% of the third. The first stock provides a continuous dividend of 1%, while the other two provide no dividends. The correlation between the first and second asset is 30%, between the second and third asset 11%, and between the first and third asset 16%. Use this data to create the BasketStockSpec structure:

AssetPrice = [56;92;125];
Sigma = [0.20;0.12;0.15];

% Create the Correlation matrix. Correlation matrices are symmetric and
% have ones along the main diagonal.
NumInst  = 3;
Corr = zeros(NumInst,1);
Corr(1,2) = .30;
Corr(2,3) = .11;
Corr(1,3) = .16;
Corr = triu(Corr,1) + tril(Corr',-1) + diag(ones(NumInst,1), 0);

% Define dividends
DivType = cell(NumInst,1);
DivType{1}='continuous';
DivAmounts = cell(NumInst,1);
DivAmounts{1} = 0.01;

Quantity = [0.25; 0.40; 0.35];

BasketStockSpec = basketstockspec(Sigma, AssetPrice, Quantity, Corr, ...
'DividendType', DivType, 'DividendAmounts', DivAmounts)
BasketStockSpec = 

             FinObj: 'BasketStockSpec'
              Sigma: [3x1 double]
         AssetPrice: [3x1 double]
           Quantity: [3x1 double]
        Correlation: [3x3 double]
       DividendType: {3x1 cell}
    DividendAmounts: {3x1 cell}
    ExDividendDates: {3x1 cell}

Examine the BasketStockSpec structure.

BasketStockSpec.Correlation
ans =

    1.0000    0.3000    0.1600
    0.3000    1.0000    0.1100
    0.1600    0.1100    1.0000

Create a Basket Stock Structure for Two Stocks

Find a basket option of two stocks. The stocks are currently trading at $60 and $55 with volatilities of 30% per annum. The basket option contains 50% of each stock. The first stock provides a cash dividend of $0.25 on May 1, 2009 and September 1, 2009. The second stock provides a continuous dividend of 3%. The correlation between the assets is 40%. Use this data to create the structure BasketStockSpec:

AssetPrice = [60;55];
Sigma = [0.30;0.30];

% Create the Correlation matrix. Correlation matrices are symmetric and
% have ones along the main diagonal.
Correlation = [1 0.40;0.40 1];

% Define dividends
NumInst  = 2;
DivType = cell(NumInst,1);
DivType{1}='cash';
DivType{2}='continuous';

DivAmounts = cell(NumInst,1);
DivAmounts{1} = [0.25 0.25];
DivAmounts{2} = 0.03;

ExDates = cell(NumInst,1);
ExDates{1} = {'May-1-2009' 'Sept-1-2009'};

Quantity = [0.5; 0.50];

BasketStockSpec = basketstockspec(Sigma, AssetPrice, Quantity, Correlation, ...
'DividendType', DivType, 'DividendAmounts', DivAmounts, 'ExDividendDates',ExDates)
BasketStockSpec = 

             FinObj: 'BasketStockSpec'
              Sigma: [2x1 double]
         AssetPrice: [2x1 double]
           Quantity: [2x1 double]
        Correlation: [2x2 double]
       DividendType: {2x1 cell}
    DividendAmounts: {2x1 cell}
    ExDividendDates: {2x1 cell}

Examine the BasketStockSpec structure.

BasketStockSpec.DividendType
ans = 

    'cash'
    'continuous'

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