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 (computation and accuracy) in solving high-dimensional optimization problems and hence 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
We introduce an artificial intelligence method, i.e., swarm intelligence, to locate the optimal exercise boundary
We propose an artificial intelligence (AI) method which is based upon the theory of swarm
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). The first approach is proposed by Longstaff and Schwartz (2001) who approximate the continuation value of the option by a regression function (its functional form can be arbitrary). 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
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