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Re: What are the boundary conditions for the Forward contract PDE?

October 9th, 2020, 3:50 pm

This is the plot with spot prices at time T (vector ST in the code) on x-axis and option prices at time 0 ((F-K)*exp(-r*T) in the code) on y-axis. As you can see the there is a problem when the option price approaches the biggest value of the spot price, since the curve goes from linear to exponential, I guess this is due to the fact that the right end condition is missing

A trick that I was using for this kind of problem: try using the boundary conditions [$]u^{N} = 2 u^{N-1} - u^{N-2} [$],  [$]u^{0} = 2 u^{1} - u^{2}[$] modelling [$]\partial_{xx}u=0[$] (linear behavior at infinity). AFAIR, this saved me to compute complex, payoff dependent, Dirichlet or Neuman boundary conditions. Obviously it only works for linear at infinity type payoff.
I don't like these BCs and I suspect the near-field BC also not correct. Fichera at  S= 0 gives du/dt + ru = 0.
It's mostly old hat at this stage.
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