A Moment Based Analytic Approximation of the Risk-neutral Density of American Options

44 Pages Posted: 25 Aug 2014 Last revised: 4 Feb 2018

Juan Arismendi Zambrano

National University of Ireland, Maynooth (NUI Maynooth) - Department of Economics; University of Reading - ICMA Centre

Marcel Prokopczuk

Leibniz Universit├Ąt Hannover - Faculty of Economics and Management; University of Reading - ICMA Centre

Date Written: August 22, 2014

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 generalised Edgeworth expansion (MGEE), where the moments of the American density are obtained by a reverse engineering application of the Longstaff and Schwartz (2001) least-squares method (LSM). 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.

Keywords: Multi-asset Risk-neutral Density, American Multi-asset Options, Higher-order Moments

JEL Classification: G13, C63

Suggested Citation

Arismendi Zambrano, Juan and Prokopczuk, Marcel, A Moment Based Analytic Approximation of the Risk-neutral Density of American Options (August 22, 2014). Applied Mathematical Finance, Volume 23, 2016 - Issue 6. Available at SSRN: https://ssrn.com/abstract=2486173 or http://dx.doi.org/10.2139/ssrn.2486173

Juan Arismendi Zambrano (Contact Author)

National University of Ireland, Maynooth (NUI Maynooth) - Department of Economics ( email )

County Kildare
Ireland
+353 17087267 (Phone)

HOME PAGE: http://https://www.maynoothuniversity.ie/economics-finance-and-accounting/

University of Reading - ICMA Centre ( email )

Whiteknights Park
P.O. Box 242
Reading, RG6 6BA
United Kingdom

Marcel Prokopczuk

Leibniz Universit├Ąt Hannover - Faculty of Economics and Management ( email )

Koenigsworther Platz 1
Hannover, 30167
Germany

University of Reading - ICMA Centre ( email )

Whiteknights Park
P.O. Box 242
Reading RG6 6BA
United Kingdom

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