Semi-parametric estimation of American option prices |
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Authors: | Patrick Gagliardini Diego Ronchetti |
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Institution: | 1. University of Lugano, Faculty of Economics, Via Buffi 13, CH-6900 Lugano, Switzerland;2. Columbia University, Graduate School of Business, 3022 Broadway, 10027 New York City, NY, USA |
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Abstract: | We introduce a novel semi-parametric estimator of American option prices in discrete time. The specification is based on a parameterized stochastic discount factor and is nonparametric w.r.t. the historical dynamics of the Markovian state variables. The historical transition density estimator minimizes a distance built on the Kullback–Leibler divergence from a kernel transition density, subject to the no-arbitrage restrictions for a non-defaultable bond, the underlying asset and some American option prices. We use dynamic programming to make explicit the nonlinear restrictions on the Euclidean and functional parameters coming from option data. We study asymptotic and finite sample properties of the estimators. |
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Keywords: | C14 C60 G13 |
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