Type

Journal Article

Authors

Alan De Genaro
Juan Arismendi Zambrano

Subjects

Mathematics

Topics
asset pricing stochastic processes semi parametric general option pricing risk management monte carlo analytical approximation

A Monte Carlo Multi-Asset Option Pricing Approximation for General Stochastic Processes (2016)

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.
Collections Ireland -> Maynooth University -> Type = Article
Ireland -> Maynooth University -> Academic Unit = Faculty of Science and Engineering: Research Institutes: Hamilton Institute
Ireland -> Maynooth University -> Academic Unit = Faculty of Social Sciences: Economics, Finance and Accounting
Ireland -> Maynooth University -> Status = Published

Full list of authors on original publication

Alan De Genaro, Juan Arismendi Zambrano

Experts in our system

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Juan Arismendi Zambrano
Maynooth University
Total Publications: 9