Boundary condition Clause Samples

Boundary condition. ‌ For the modified Black-Scholes equation, we have u(−∞, t) = 0, u(x, t) = exerτ as x → ∞ for a call option, and u(−∞, t) = 1, u(x, t) = 0 as x → ∞ 1. The boundary condition at the boundary points are an approximation to the above far field boundary condition. In practice, we don’t even use this boundary condition. Indeed, if we want to know u(xk, n∆t), we can find the numerical domain of this quantity, which is the triangle {(j∆x, m∆t) | |j − k| ≤ n − m} We only need to compute u in this domain, which needs no boundary data.