WIAS Preprint No. 808, (2003)

Numerical analysis of Monte Carlo finite difference evaluation of Greeks



Authors

  • Milstein, Grigori N.
  • Tretyakov, Michael V.

2010 Mathematics Subject Classification

  • 60H30 65C30 91B28

Keywords

  • Derivative pricing and hedging, probabilistic representations, weak approximation of solutions of stochastic differential equations, Monte Carlo simulation

Abstract

An error analysis of approximation of derivatives of the solution to the Cauchy problem for parabolic equations by finite differences is given taking into account that the solution itself is evaluated using weak-sense numerical integration of the corresponding system of stochastic differential equations together with the Monte Carlo technique. It is shown that finite differences are effective when the method of dependent realizations is exploited in the Monte Carlo simulations. This technique is applicable to evaluation of Greeks. In particular, it turns out that it is possible to evaluate both the option price and deltas by a single simulation run that reduces the computational costs. Results of some numerical experiments are presented.

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