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Ikonen and Toivanen don't say that the LCP is solved exactly, they simply say that the modified back-substitution is a valid algorithm to solve the LCP. A numerical error may arise around the location of optimal exercise, since it does not fall directly on the finite difference grid. I think that however, the error is of the same order as the discretization ...


Some terms are not explained in the restricted screenshot provided like $\beta$ and $\gamma$ however, from What I see documented, my suspect is that they are using a Taylor expansion (2nd order) to proxy the generic variation of B after a change in r and t (hint: they indeed assume that B is differentiable at least one time with respect to t). It is also ...


Please see below: Copied from Quantitative Methods in Derivative Pricing by Tavella.

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