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Published / Preprint: The Effect of Non-Smooth Payoffs on the Penalty Approximation of American Options. (arXiv:1008.0836v2 [q-fin.PR] UPDATED)

May 22, 2012 by MoneyScience   Comments (0)

This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for sufficiently smooth obstacles is well established in the literature, sharp rates of convergence and particularly the effect of gradient discontinuities (i.e. the omni-present `kinks' in option payoffs) on this rate have not been fully analysed so far. This effect...

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