function u_inf = u_p_inf_call(x,tau,k)
% U_P_INF_CALL - the transformed boundary condition at x=+\infty for a call 
%   
% 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.
% 
%-----

% the most naive approximation
%u_inf = exp( 0.25*((k+1)^2)*tau ) * max( exp( 0.5*(k+1)*x ) - exp( 0.5*(k-1)*x ), 0 );

% suggested as a boundary condition on epage 58 Equation~3.12 of wilmott's book ... performs very poorly 
%u_inf = exp( 0.25*((k+1)^2)*tau ) * exp( 0.5*(k+1)*x );

% with a boundary condition derived from put-call parity
u_inf = exp( 0.25*((k+1)^2)*tau ) * ( exp( 0.5*(k+1)*x ) - exp( 0.5*(k-1)*x )*exp( -k*tau ) );