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Abstract
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In the setting of American option pricing, we introduce an efficient stochastic optimization algorithm to find the optimal exercise boundary among a parametric family. We use the Calculus of Variations to write down a probabilistic representation of the payout sensitivity with respect to the exercise boundary parameter. To use this representation in a Monte Carlo estimator, we develop an accurate stochastic differential equation discretization scheme for stopped diffusions. As an intermediate result, we are able to approximate deltas at the boundary for barrier options. We present numerical simulations and numerical analysis of the algorithms. |
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