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Binomial options pricing has no closed-form solution. (English) Zbl 1250.91098

Summary: We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach. Our proof follows from Gosper’s algorithm.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
68Q25 Analysis of algorithms and problem complexity
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
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