As luck would have it, I am now building a binomial lattice pricing model that employs the concepts of risk neutral valuation, risk free rate and expected option values at a given time step. I am approaching the problem from a computational angle; I am investigating the computational efficiency and complexity of the resulting algorithm as well as the parallelizability of the code. For each node in the lattice I aim to calculate the polynomial representing the probability function. Summing these node polynomials for a given time step and applying backwardation should yield the net present value of the of the option. The scope of this investigation is limited to European call options, but with more work I should be able to extend this to price American options.
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