Option pricing, maturity randomization and distributed computing

  • Authors:

  • Gianluca Fusai;Daniele Marazzina;Marina Marena

  • Affiliations:

  • Universití degli Studi del Piemonte Orientale "A. Avogadro", Department of Economic Science and Quantitative Methods SEMeQ, Novara, Italy;Politecnico di Milano, Department of Mathematics "F. Brioschi", Milano, Italy;Universití degli Studi di Torino, Department of Statistics and Applied Mathematics "D. De Castro", Torino, Italy

  • Venue:
  • Parallel Computing
  • Year:
  • 2010

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Abstract

We price discretely monitored options when the underlying evolves according to different exponential Levy processes. By geometric randomization of the option maturity, we transform the n-steps backward recursion that arises in option pricing into an integral equation. The option price is then obtained solving n independent integral equations by a suitable quadrature method. Since the integral equations are mutually independent, we can exploit the potentiality of a grid computing architecture. The primary performance disadvantage of grids is the slow communication speeds between nodes. However, our algorithm is well-suited for grid computing since the integral equations can be solved in parallel, without the need to communicate intermediate results between processors. Moreover, numerical experiments on a cluster architecture show the good scalability properties of our algorithm.