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An Analytic Approximation of the Implied Risk-Neutral Density of American Multi-Asset Options

Juan Arismendi Zambrano () and Marcel Prokopczuk ()

ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading

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 can not be applied. In this paper, we derive a model-free analytical formula for the implied risk-neutral density 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 (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
Date: 2014-08
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