Monte Carlo Simulation of the CGMY Process and Option Pricing. Issue 12 (30th January 2014)

• Record Type: Journal Article
• Authors: Ballotta, Laura; Kyriakou, Ioannis
• Is Part Of: Journal of futures markets. Volume 34:Issue 12(2014:Dec.)
• Page Start: 1095
• Page End: 1121
• Publication Date: 2014-01-30
• Subjects: Commodity exchanges -- Periodicals; Foreign exchange futures -- Periodicals; 332.632
• DOI: 10.1002/fut.21647
• Languages: English
• ISSNs: 0270-7314

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <sec id="fut21647-sec-0001" sec-type="section"> <p>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</p> </sec> </abstract>