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basketbyls - Price 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 the strike price.
`Settle`	Scalar of the settlement or trade date specified as a string or serial date number.
`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 per trial. 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

Outputs

Price

Price of the basket option.

Examples

Find an American call basket option of three stocks. The stocks are currently trading at $35, $40 and $45 with annual volatilities of 12%, 15% and 18%, respectively. The basket contains 33.33% of each stock. Assume the correlation between all pair of assets is 50%. On May 1, 2009, an investor wants to buy a three-year call option with a strike price of $42. The current annualized continuously compounded interest rate is 5%. Use this data to compute the price of the call basket option using the Longstaff-Schwartz model.

Settle = 'May-1-2009';
Maturity  = 'May-1-2012';

% 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.
Corr = [1 0.50 0.50; 0.50 1 0.50;0.50 0.50 1];

% Define BasketStockSpec
AssetPrice =  [35;40;45]; 
Volatility = [0.12;0.15;0.18];
Quantity = [0.333;0.333;0.333];
BasketStockSpec = basketstockspec(Volatility, AssetPrice, Quantity, Corr);

% Compute the price of the call basket option
OptSpec = {'call'};
Strike = 42;
AmericanOpt = 1; % American option
Price = basketbyls(RateSpec, BasketStockSpec, OptSpec, Strike, Settle, Maturity,...
'AmericanOpt',AmericanOpt)

This returns:

Price =

   5.60499

Increase the number of simulation trials to 2000 to give the following results:

NumTrial = 2000;
Price = basketbyls(RateSpec, BasketStockSpec, OptSpec, Strike, Settle, Maturity,...
'AmericanOpt',AmericanOpt,'NumTrials',NumTrial)
Price =

   5.6665

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.