Abstract
The purpose of this paper is to develop a new non-parametric method to price options based on normalized Multipoint Pade Approximants. Following the seminal paper of Pade (1892), we propose to approximate the risk-neutral distribution by a rational function of polynomials that can accommodate the asymmetric and leptokurtic characteristics of the implied state price densities. After recalling the general framework of Pade Approximants we present an analytical formula where we use a power series expansion of the risk-neutral density in order to infer the coefficients of the rational function of polynomials. A suitable alternative to this method will be to use various points of local expansion, resulting from the capability of the Pade to respect such a confluence. By manipulating the base option pricing formula with risk-neutral density (see Cox and Ross, 1976), both of these methods is implicitly satisfying the martingale constraint (see Longstaff, 1995 and Jurczenko, et al., 2006). We then investigate from simulated option prices the shape of the risk-neutral density Pade approximations to compare their radius of convergence.
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