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    A moment-based analytic approximation of the risk-neutral density of American options


    Arismendi Zambrano, Juan and Prokopczuk, Marcel (2014) A moment-based analytic approximation of the risk-neutral density of American options. Applied Mathematical Finance, 23 (6). pp. 409-444. ISSN 1350-486X

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    Abstract

    The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied risk-neutral density based on the implied moments of the implicit European contract under which the expected value will be the price of the equivalent payoff with the American exercise condition. The risk-neutral density is semi-parametric as it is the result of applying the multivariate generalized Edgeworth expansion, where the moments of the American density are obtained by a reverse engineering application of the least-squares method. The theory of multivariate truncated moments is employed for approximating the option price, with important consequences for the hedging of variance, skewness and kurtosis swaps.

    Item Type: Article
    Additional Information: Cite as: J. C. Arismendi & Marcel Prokopczuk (2016) A moment-based analytic approximation of the risk-neutral density of American options, Applied Mathematical Finance, 23:6, 409-444, DOI: 10.1080/1350486X.2017.1297726
    Keywords: Multi-asset risk-neutral density; American multi-asset options; higher order moments;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 10208
    Identification Number: https://doi.org/10.1080/1350486X.2017.1297726
    Depositing User: Juan Arismendi Zambrano
    Date Deposited: 12 Nov 2018 15:10
    Journal or Publication Title: Applied Mathematical Finance
    Publisher: Taylor & Francis
    Refereed: Yes
    URI:

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