A Monte Carlo Multi-Asset Option Pricing Approximation for General Stochastic Processes

Chaos, Solitons & Fractals, Forthcoming

44 Pages Posted: 25 Apr 2014 Last revised: 18 Feb 2016

See all articles by Juan Arismendi-Zambrano

Juan Arismendi-Zambrano

National University of Ireland (Maynooth University) - School of Business; University of Reading - ICMA Centre

Alan Genaro

Getulio Vargas Foundation (FGV) - Sao Paulo School of Business Administration

Date Written: April 23, 2014

Abstract

We derived a model-free analytical approximation of the price of a multi-asset option defined over an arbitrary multivariate process, applying a semi-parametric expansion of the unknown risk-neutral density with the moments. The analytical expansion termed as the Multivariate Generalised Edgeworth Expansion (MGEE) is an infinite series over the derivatives of an auxiliary continuous time density. The expansion could be used to enhance a Monte Carlo pricing methodology incorporating the information about moments of the risk-neutral distribution. The efficiency of the approximation is tested over a jump-diffusion and a q-Gaussian diffusion. For the known density, we tested the multivariate lognormal (MVLN), even though arbitrary densities could be used. The MGEE relates two densities and isolates the effects of multivariate moments over the option prices. Results show that a calibrated approximation provides a good fit when the difference between the moments of the risk-neutral density and the auxiliary density are small relative to the density function of the former, and the uncalibrated approximation has immediate implications over risk management and hedging theory. The possibility to select the auxiliary density provides an advantage over classical Gram–Charlier A, B and C series approximations.

Keywords: Multi-asset option pricing, Multivariate Risk Management, Edgeworth Expansion, Higher-order Moments

Suggested Citation

Arismendi-Zambrano, Juan and Genaro, Alan, A Monte Carlo Multi-Asset Option Pricing Approximation for General Stochastic Processes (April 23, 2014). Chaos, Solitons & Fractals, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2428216 or http://dx.doi.org/10.2139/ssrn.2428216

Juan Arismendi-Zambrano (Contact Author)

National University of Ireland (Maynooth University) - School of Business ( email )

Room 65, Rhetoric House, Maynooth University
Maynooth, Kildare W23 HW31
Ireland
+353 17087267 (Phone)
W23 HW31 (Fax)

HOME PAGE: http://https://www.maynoothuniversity.ie/school-business

University of Reading - ICMA Centre ( email )

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

Alan Genaro

Getulio Vargas Foundation (FGV) - Sao Paulo School of Business Administration ( email )

Sao Paulo
BRAZIL

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