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Chooser Option

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Description

A Chooser option gives the owner the choice at some fixed future date (before expiration) to pick either a vanilla call or put option. In a simple chooser option, the call and put have both the same strike and expiration date.

ThetaML implementation of a chooser option

The model 'chooser' computes the chooser option price. The underlying 'S' and the discount numeraire 'EUR' are processes simulated externally. For example, the process 'S' can be a stock price process that follows a Geometric Brownian Motion or a Heston Volatility process. The discount numeraire 'EUR' can be a constant discount curve as implemented in Discounting, or a stochastic process that has a dynamics as defined in the CIR model.

% The model chooser computes the value of the option to
% choose a put or a call option at time t = 0.5
model chooser
    import S    "Underlying stock prices"
    import EUR  "Discount numeraire"
    import K    "Option strike price"
    export V    "Option value"
 
    %at current time, set the option value to have the same expected discounted
    %value as the variable 'V'; the ThetaML future operator '!' accompanying the
    %variable 'V' acts like a function on 'V', such that the values of 'V'at 
    %current time remain to be determined at a later instance when 'V' is assigned 
    %some values
    P = E(V!)
    %the ThetaML command 'theta' passes time by '0.5' years
    theta 0.5
    %chooser option, if the expected discounted values of 'V1!' is larger than that of 'V2!'
    if E(V1!) > E(V2!)
       V = V1!
    else
       V = V2!
    end
    %the ThetaML command 'theta' passes time by '0.5' years
    theta 0.5
    %at option maturity time 1, set the option payoffs;
    %the option payoffs are discounted to time 0 by the discount numeraire 'EUR'
    V1 = max(K - S, 0) * EUR
    V2 = max(S - K, 0) * EUR
end


Thetagram graphic illustration of modelling chooser option


Chooser.png