Abstract
In this paper, we evaluate American-style, path-dependent derivatives with an artificial intelligence technique. Specifically, we use swarm intelligence to find the optimal exercise boundary for an American-style derivative. Swarm intelligence is particularly efficient (regarding computation and accuracy) in solving high-dimensional optimization problems and hence, is perfectly suitable for valuing complex American-style derivatives (e.g., multiple-asset, path-dependent) which require a high-dimensional optimal exercise boundary.
Highlights
Evaluating American-style derivatives is a challenging task
Once the derivative contract is written on multiple assets, lattice models become infeasible
We introduce an artificial intelligence method, i.e., swarm intelligence, to locate the optimal exercise boundary
Summary
Evaluating American-style derivatives is a challenging task. In a univariate setting (e.g., option on one stock), lattice models—either the binomial model (e.g., Cox et al 1979) or finite difference methods (e.g., see Hull 2015)—are an efficient method. once the derivative contract is written on multiple assets (e.g., exchange options), lattice models become infeasible (with regard to both computation time and memory space). If the continuation value can be reasonably and accurately estimated, the early exercise problem can be solved and one can readily compute the value of an American-style derivative. The drawback of this approach is apparent—it is hard to know in advance which functional form of the regression will provide an accurate estimate for the continuation value. If we can accurately estimate the boundary, the value of an American-style derivative can be calculated, as it would be a barrier option2 This approach is more computationally efficient than the Longstaff–Schwartz model; yet, it suffers the same drawback of the Longstaff–Schwartz model—the accuracy of the American-style derivative value relies upon an accurate exercise boundary. In the case of a truly free boundary (i.e., piecewise), we find that PSO can ideally provide the best solution to complex (e.g., American-style, multi-asset, path-dependent) derivatives problems
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