Derivative price can be calculated either by analytic formula like Black Scholes model, or by numerical solution, for instance, solving paritial difference equation, Monte carlo simulation, binomial tree, etc. A lot of people are not aware of this simple trick to avoid oscillation in binomial trees. Oscillation might become dangerous when calculating Greeks via numerical differentiation. Here's the trick. E.g., for American options, just replace the last step in the binomial tree with the closed-form Black-Scholes formula.

http://leippold.googlepages.com/matlab for details.
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