Skip to main content

An Analytic Approximation of the Implied Risk-neutral Density of American Multi-asset Options

The price of a European option can be computed as the expected value of the payoff function under the riskneutral 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.

Published on 30th August 2014
Authors Juan C Arismendi Z, Marcel Prokopczuk
Series Reference ICM-2014-07