Optimal convergence rate of the explicit finite difference scheme for American option valuation

An optimal convergence rate O(@Dx) for an explicit finite difference scheme for a variational inequality problem is obtained under the stability condition @s^[email protected]@Dx^2=<1 using completely PDE methods. As a corollary, a binomial tree scheme of an American put option (where @s^[email protected]@Dx^2=1) is convergent unconditionally with the rate O((@Dt)^1^/^2).

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