hard · Quantitative Finance numerical
In a finite-difference grid, the boundary condition for a European call option as S to ∞ is often approximated as V(S, t) ≈ S - Ke^-r(T-t).
How is this typically implemented at the final grid node i = i_max?
- By requiring the second derivative to be zero, (partial^2 V)/(partial S^2) = 0, at the boundary.
- By setting the value V_i_max^n to S_max - Ke^-r(T-t) at each time step.
- By setting V_i_max^n = V_i_max-1^n to simulate a reflecting boundary.
- By using a 'ghost node' and requiring (partial V)/(partial t) = 0 at the boundary.
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