Basket Option

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Basket option

A Basket option is an option on a portfolio of underlyings. Many different formulations of basket options are in use. Examples are options with a payoff dependent on the average performance of the underlyings or on the performance of the best asset.

Examples

Rainbow Option

A Rainbow option gives the owner the right to buy (resp. sell) the maximum (resp. minimum) of two underlying assets for a fixed value K. 

%% A Rainbow option gives the owner the right to buy 
%% the maximum (resp. minimum) of two underlying assets 
%% for K.
model Rainbow
    import S    "Stock Price"
    import EUR  "Numeraire"
    import K    "Strike"
    export P    "Option value"
 
    P = E(V!)
 
    Theta 1
 
    V = max(max(S[1],S[2])-K,0)    
end

American Basket option

In the following example we look at a basket option with an early exercise opportunity after 0.5 years and which can handle arbitrary many underlyings. 

%% Basket option with multiple underlyings and 
%% a payoff dependent which depends on the
%% the maximal call price of each underlying 
model Basket
    import S    "Stock Price"
    import EUR  "Numeraire"
    import K    "Strike"
    export P    "Option value"
 
    P = E(V!)
 
    Theta 1/2
 
    % compute exercise price
    ex_price = 0
    loop s,k:S,K 
        ex_price = max(ex_price, (s-k)*EUR )
    end
 
    % if optimal to exercise, exercise
    if E(V!) < ex_price 
        V = size(ex_price)
    end 
 
    Theta 1/2
 
    ex_price = 0
    loop s,k:S,K 
        ex_price = max(ex_price, (s-k)*EUR )
    end
    V = ex_price    
end
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