Numerical analysis of Monte Carlo evaluation of Greeks by finite differences

Grigori N. Milstein and Michael V. Tretyakov

Journal of Computational Finance

Abstract: ABSTRACT An error analysis of approximation of deltas (derivatives of the solution to the Cauchy problem for parabolic equations) by finite differences is given, taking into account that the value of the hedging portfolio itself (the solution of the problem) 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. Evaluation of other Greeks is also considered. Results of numerical experiments, including those with Heston stochastic volatility model, are presented.

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