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basketsensbyls - Calculate price and sensitivities for basket options using Longstaff-Schwartz model

Syntax

Price = basketbyls(RateSpec, BasketStockSpec, OptSpec, Strike, Settle, ExerciseDates) Price = basketbyls(RateSpec, BasketStockSpec, OptSpec, Strike, Settle, ExerciseDates, 'ParameterName', ParameterValue ...)

Description

Price = basketbyls(RateSpec, BasketStockSpec, OptSpec, Strike, Settle, ExerciseDates) prices basket options using the Longstaff-Schwartz model.

Price = basketbyls(RateSpec, BasketStockSpec, OptSpec, Strike,Settle, ExerciseDates, '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.

Inputs

`RateSpec`	Annualized, continuously compounded rate term structure. For more information on the interest rate specification, see `intenvset`.
`BasketStockSpec`	`BasketStock` specification. For information on the basket of stocks specification, see `basketstockspec`.
`OptSpec`	String or `2`-by-`1` cell array of the strings `'call'` or `'put'`.
`Strike`	The option strike price: For a European or Bermuda option, `Strike` is a scalar (European) or `1`-by-`NSTRIKES` (Bermuda) vector of strike price. For an American option, `Strike` is a scalar vector of strike price.
`Settle`	Scalar of settlement or trade date.
`ExerciseDates`	The exercise date for the option: For a European or Bermuda option, `ExerciseDates` is a `1`-by-`1` (European) or `1`-by-`NSTRIKES` (Bermuda) vector of exercise dates. For a European option, there is only one `ExerciseDate` on the option expiry date. For an American option, `ExerciseDates` is a `1`-by-`2` vector of exercise date boundaries. The option exercises on any date between or including the pair of dates on that row. If there is only one non-`NaN` date, or if `ExerciseDates` is `1`-by-`1`, the option exercises between the `Settle` date and the single listed `ExerciseDate`.

Parameter–Value Pairs

`AmericanOpt`	Parameter values are a scalar flag. 0 — European/Bermuda 1 — American Default: 0
`NumPeriods`	Parameter value is a scalar number of simulation periods. `NumPeriods` is considered only when pricing European basket options. For American and Bermuda basket options, `NumPeriod` equals the number of exercise days during the life of the option. Default: 100
`NumTrials`	Parameter value is a scalar number of independent sample paths (simulation trials). Default: 1000
`OutSpec`	Parameter value is an `NOUT`-by-`1` or `1`-by-`NOUT` cell array of strings 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', 'Lamba', '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'}`
`UndIdx`	Scalar of the indice of the underlying instrument to compute the sensitivity. Default: `UndIdx` = `[]`

Outputs

PriceSens

Expected prices or sensitivities values.

Examples

Find a European put basket option of two stocks. The basket contains 50% of each stock. The stocks are currently trading at $90 and $75, with annual volatilities of 15%. Assume that the correlation between the assets is zero. On May 1, 2009, an investor wants to buy a one-year put option with a strike price of $80. The current annualized, continuously compounded interest is 5%. Use this data to compute price and delta of the put basket option with the Longstaff-Schwartz 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  = 2;
InstIdx = ones(NumInst,1);
Corr = diag(ones(NumInst,1), 0);

% Define BasketStockSpec
AssetPrice =  [90; 75]; 
Volatility = 0.15;
Quantity = [0.50; 0.50];
BasketStockSpec = basketstockspec(Volatility, AssetPrice, Quantity, Corr);

% Compute the price of the put basket option. Calculate also the delta 
% of the first stock.
OptSpec = {'put'};
Strike = 80;
OutSpec = {'Price','Delta'}; 
UndIdx = 1; % First element in the basket
                                     
[Price, Delta] = basketsensbyls(RateSpec, BasketStockSpec, OptSpec,...
Strike, Settle, Maturity,'OutSpec', OutSpec,'UndIdx', UndIdx)

This returns:

Price =

   1.08519

Delta =

  -0.10311

Compute the Price and Delta of the basket with a correlation of -20%:

NewCorr = [1 -0.20; -0.20 1];

% Define the new BasketStockSpec.
BasketStockSpec = basketstockspec(Volatility, AssetPrice, Quantity, NewCorr);

% Compute the price and delta of the put basket option. 
[Price, Delta] = basketsensbyls(RateSpec, BasketStockSpec, OptSpec,...
Strike, Settle, Maturity,'OutSpec', OutSpec,'UndIdx', UndIdx)

Price =

   0.83903

Delta =

  -0.08847

References

Longstaff, F.A., and E.S. Schwartz, "Valuing American Options by Simulation: A Simple Least-Squares Approach", The Review of Financial Studies,Vol. 14, No. 1, Spring 2001, pp. 113–147.