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Determine European basket options price or sensitivities using Nengjiu Ju approximation model


PriceSens = basketsensbyju(RateSpec,BasketStockSpec,OptSpec,Strike,Settle,Maturity)
PriceSens = basketsensbyju(RateSpec,BasketStockSpec,OptSpec,Strike,Settle,Maturity,'ParameterName',ParameterValue, ...)


PriceSens = basketsensbyju(RateSpec,BasketStockSpec,OptSpec,Strike,Settle,Maturity) calculates prices or sensitivities for basket options using the Nengjiu Ju approximation model.

PriceSens = basketsensbyju(RateSpec,BasketStockSpec,OptSpec,Strike,Settle,Maturity,'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 matches are allowable, if no ambiguities exist.

Input Arguments


Annualized, continuously compounded rate term structure. For more information on the interest rate specification, see intenvset.


BasketStock specification. For information on the basket of stocks specification, see basketstockspec.


Character vector or a 2-by-1 cell array of character vectors with values of 'call' or 'put'.


Scalar of the option strike price.


Scalar of the settlement or trade date specified as a character vector or serial date number.


Maturity date, specified as a character vector or serial date number.

Parameter–Value Pairs


Parameter value is an NOUT-by-1 or 1-by-NOUT cell array of character vectors indicating the nature and order of the outputs for the function. Possible values are 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'. For example, OutSpec = {'Price', 'Lambda', 'Rho'} specifies that the output is Price, Lambda, and Rho, in that order.

OutSpec = {'All'} specifies that the output should be Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec as OutSpec = {'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', 'Price'};.

Default: OutSpec = {'Price'}


Scalar of the indice of the underlying instrument to compute the sensitivity.

Default: UndIdx = []

Output Arguments


Expected prices or sensitivities values for the basket option.


collapse all

Find a European call basket option of five stocks. Assume that the basket contains:

  • 5% of the first stock trading at $110

  • 15% of the second stock trading at $75

  • 20% of the third stock trading at $40

  • 25% of the fourth stock trading at $125

  • 35% of the fifth stock trading at $92

These stocks have annual volatilities of 20% and the correlation between

the assets is zero. On May 1, 2009, an investor wants to buy a 1-year

call option with a strike price of $90. The current annualized, continuously

compounded interest is 5%. Use this data to compute price and delta of

the call basket option with the Ju approximation model.

Settle = 'May-1-2009';
Maturity  = 'May-1-2010';

% Define RateSpec
Rate = 0.05;
Compounding = -1;
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', ...
Settle, 'EndDates', Maturity, 'Rates', Rate, 'Compounding', Compounding);

% Define the Correlation matrix. Correlation matrices are symmetric, and
% have ones along the main diagonal.
NumInst  = 5;
InstIdx = ones(NumInst,1);
Corr = diag(ones(5,1), 0);

% Define BasketStockSpec
AssetPrice =  [110; 75; 40; 125; 92]; 
Volatility = 0.2;
Quantity = [0.05; 0.15; 0.2; 0.25; 0.35];
BasketStockSpec = basketstockspec(Volatility, AssetPrice, Quantity, Corr);

% Compute the price of the call basket option. Calculate also the delta 
% of the first stock.
OptSpec = {'call'};
Strike = 90;
OutSpec = {'Price','Delta'}; 
UndIdx = 1; % First element in the basket
[Price, Delta] = basketsensbyju(RateSpec, BasketStockSpec, OptSpec, Strike, Settle, ...
Maturity, 'OutSpec', OutSpec,'UndIdx', UndIdx)
Price = 5.1610
Delta = 0.0297

Compute Delta with respect to the second asset:

UndIdx = 2; % Second element in the basket
OutSpec = {'Delta'}; 
Delta = basketsensbyju(RateSpec, BasketStockSpec, OptSpec, Strike, Settle, Maturity, ...
Delta = 0.0906


Nengjiu Ju. “Pricing Asian and Basket Options Via Taylor Expansion.” Journal of Computational Finance. Vol. 5, 2002.

Introduced in R2009b

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