Germano, G; Engel, M; Scalas, E; (2006) City@home: Monte Carlo derivative pricing distributed on networked computers. Proceedings of Science , 26 , Article 011.

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Abstract

Monte Carlo is a powerful and versatile derivative pricing tool, with the main drawback of requiring a large amount of computing time to generate enough realisations of the stochastic process. However, since realisations are independent from each other, the task is “embarrassingly” parallel and the workload can be easily distributed on a large set of processors without the need for fast networking and thus an expensive dedicated supercomputer. Such an alternative, much cheaper and more accessible way can be realised with the BOINC toolkit, distributing the Monte Carlo runs on networked clients running under Windows, Linux or various Unix variants, and recollecting the results at the end for a statistical evaluation of the price distribution at the final time. Though it is likely that the clients will belong to the intranet of a large company or institution, we gave our program the evocative name City@home in honour of the paradigmatic SETI@home project. As an application, we present the generation of synthetic high frequency financial time series for speculative option valuation in the context of uncoupled continuous-time random walks (fractional diffusion), with a Lévy marginal density function for the tick-by-tick log returns and a Mittag-Leffler marginal density function for the waiting times. Lévy deviates are generated with the Chambers-Mallows-Stuck method, Mittag-Leffler deviates with the Kozubowski-Pakes method.

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