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Description: |
Under mild assumptions, this paper proposes a novel representation for the early exercise boundary of American-style double knock-out options in terms of the simpler optimal stopping boundary of a nested single barrier American-style contract. Therefore, and from now on, any single-factor time-homogeneous and Markovian valuation model that offers pricing solutions for American-style single barrier options can be easily extended to price the more complex double barrier contracts. Additionally, and as a by-product of the novel representation obtained for the optimal stopping boundary, we are able to provide new put-call duality relations for American-style double knock-out options, under the whole class of exponential Lévy models. To illustrate the practical relevance of our novel results, we extend the static hedge portfolio approach (under pure diffusive processes) as well as the COS approximation (for option pricing models with jumps) to the valuation of American-style double knock-out options. In the first case, we just adapt the smooth-pasting recurrence conditions attached to a nested single barrier contract. For the COS approximation, we simply adjust the Fourier-cosine series coefficients of the option price.
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