American put option with jump-diffusion can be modelled as a vari- ational inequality problem with an integral term.Under the stability condition （σ2Δt）/（Δx2）≤1,whereΔx=ln（Sn+1）/（Sn）,the convergence rate O(（Δx）2/3+（Δt）1/3)of the explicit finite scheme for this problem is obtained by using penalization technique. The binomial tree scheme of this model,which is equivalent to the explicit scheme, is convergent by the same rate.
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