Monte Carlo simulations with vectorial Milstein discretization for derivatives pricing in multi-factor stochastic model

Tiberiu Socaciu

Abstract


In this paper we describe a tool for processing stochastic differential equations for financial engineering in terms of computer algebra (symbolic calculus) and numerical calculus (numeric approach). The software generate formulas for Milstein discretizations (see [1]) of vectorial stochastic differential equations and computing simulation paths in Monte Carlo simulation processes.


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References


KLOEDEN, P.E., PLATEN, E. Numerical Solution of Stochastic Differential Equations. Springer, Berlin. 1999, ISBN 3-540-54062-8.

ZAHRI, M. Multidimensional Milstein scheme for solving a stochastic model for prebiotic evolution. In Journal of Taibah University for Science, 2014, Vol. 8, Issue 2, April 2014, pp. 186–198.

SOCACIU, T. Pricing in Heston like framework. Post-doctoral thesis (draft, in progress), Romanian Academy, Bucuresti.

SOCACIU, T., Calcul simbolic. Procesor si preprocesor de expresii Poisson cu aplicatii in mecanica cereasca. University of Cluj, thesis, 1996.

SOCACIU, Tiberiu. Tool for symbolic generation of discretization formlaes used in Monte Carlo simulations in multiasset vectorial differential stochastic equations. FIBA 2015, XIII edition, March 26-27, 2015, Bucharest, Romania.

HESTON, Steven L. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. In The Review of Financial Studies, 1993, 6 (2): 327–343, doi:10.1093/rfs/6.2.327. JSTOR 2962057.

RÖßLER, A. Runge–Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations. In SIAM Journal on Numerical Analysis, 2010, 48 (3): 922. doi:10.1137/09076636X.

BAYER, Christian. Discretization of SDEs: Euler Methods and Beyond. At PRisMa 2006 Workshop, 09-26-2006. Available at https://people.kth.se/~cbayer/files/euler_talk_handout.pdf, last access in nov 2014.

TANAKA, Hideyuki, YAMADA, Toshihiro. Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method, 29 nov 2013. Available at http://arxiv.org/pdf/1210.0670v2.pdf, last access in nov 2014.


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