basketstockspec

Specify basket stock structure using Longstaff-Schwartz model

Syntax

BasketStockSpec = basketstockspec(Sigma,AssetPrice,Quantity,Correlation)

BasketStockSpec = basketstockspec(___,Name,Value)

Description

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

BasketStockSpec = basketstockspec(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

Examples

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 = struct with fields:
             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 = 3×3

    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 = struct with fields:
             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 = 2x1 cell
    {'cash'      }
    {'continuous'}

Input Arguments

Sigma — Annual price volatility of the underlying security

vector in decimals

Annual price volatility of the underlying security, specified as an NINST-by-1 vector in decimals.

Data Types: double

AssetPrice — Underlying asset price values at time 0

vector

Underlying asset price values at time 0, specified as a NINST-by-1 vector.

Data Types: double

Quantity — Quantities of the instruments contained in the basket

vector

Quantities of the instruments contained in the basket, specified as an NINST-by-1 vector.

Data Types: double

Correlation — Correlation values

matrix

Correlation values, specified as an NINST-by-1 matrix.

Data Types: double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: BasketStockSpec = basketstockspec(Sigma,AssetPrice,Quantity,Correlation,'DividendType',DivType,'DividendAmounts',DivAmounts)

'DividendAmounts' — Dividend amounts for basket instruments

row vector

Dividend amounts for basket instruments, specified as the comma-separated pair consisting of 'DividendAmounts' and an NINST-by-1 cell array. 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.

Data Types: double

'DividendType' — Stock dividend type

cell array of character vectors

Stock dividend type, specified as the comma-separated pair consisting of 'DividendType' and an NINST-by-1 cell array of character vectors specifying each stock's dividend type. Dividend type must be either cash for actual dollar dividends or continuous for continuous dividend yield.

Data Types: char | cell

'ExDividendDates' — Ex-dividend dates for the basket instruments

cell array

Ex-dividend dates for the basket instruments, specified as the comma-separated pair consisting of 'ExDividendDates' and an 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.

Data Types: cell

Output Arguments

BasketStockSpec — Structure encapsulating the properties of a basket stock structure

structure

Structure encapsulating the properties of a basket stock structure, returned as a structure.