function g = tran_payoff_put(xgrid,tau,k)
% TRAN_PAYOFF_PUT - the transformed payoff for a put 
%                    see page 166 of Wilmott's book (epage 184)
%   
% Checked: 2008-11-16 ... no errors found 
% 
% Written by:
% -- 
% John L. Weatherwax                2008-06-11
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% convert to a column vector: 
xgrid = xgrid(:); 
nx    = length(xgrid); 

% the transformed payoff: 
g = exp( 0.25*((k+1)^2)*tau ) * max( [ exp( 0.5*(k-1)*xgrid ) - exp( 0.5*(k+1)*xgrid ), zeros(nx,1) ], [], 2 ); 

% special cases for the endpoints: 
%%%g(1)   = exp( 0.25*((k+1)^2)*tau ) * exp( 0.5*(k-1)*xgrid(1) ) * exp( -k*tau );
%%%g(end) = 0.0;