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Monte Carlo Simulation of the CGMY Process and Option Pricing
Author(s) -
Ballotta Laura,
Kyriakou Ioannis
Publication year - 2014
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.21647
Subject(s) - monte carlo method , univariate , mathematics , valuation of options , importance sampling , rejection sampling , computer science , mathematical optimization , statistical physics , hybrid monte carlo , econometrics , multivariate statistics , markov chain monte carlo , statistics , physics
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. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 34:1095–1121, 2014