Monte carlo simulation of the CGMY process and option pricing

Ballotta, L. & Kyriakou, I. (2014). Monte carlo simulation of the CGMY process and option pricing. Journal of Futures Markets, doi: 10.1002/fut.21647

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Abstract

We present a joint Monte Carlo-Fourier transform sampling scheme for pricing derivative products under a Carr–Geman–Madan–Yor (CGMY) model (Carr et al. [Journal of Business, 75, 305–332, 2002]) exhibiting jumps of infinite activity and finite or infinite variation. The approach relies on numerical transform inversion with computable error estimates, which allow generating the unknown cumulative distribution function of the CGMY process increments at the desired accuracy level. We use this to generate samples and simulate the entire trajectory of the process without need of truncating the process small jumps. We illustrate the computational efficiency of the proposed method by comparing it to the existing methods in the literature on pricing a wide range of option contracts, including path-dependent univariate and multivariate products.

Item Type: Article
Additional Information: This is the accepted version of the following article: Ballotta, L. and Kyriakou, I. (2014), Monte Carlo Simulation of the CGMY Process and Option Pricing. J. Fut. Mark., which has been published in final form at http://dx.doi.org/10.1002/fut.21647. Article in press.
Subjects: H Social Sciences > HG Finance
Divisions: Cass Business School > Faculty of Finance
URI: http://openaccess.city.ac.uk/id/eprint/3976

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