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Efficient price sensitivity estimation of financial derivatives by weak derivatives

Author

Listed:
  • Kloeden Peter E.

    (Department of Mathematics, Goethe University Frankfurt, Frankfurt am Main, Germany.)

  • Sanz-Chacón Carlos

    (Department of Mathematics and Goethe Center for Scientific Computing (G-CSC), Goethe University Frankfurt, Frankfurt am Main, Germany.)

Abstract

The stochastic gradient estimation method of weak derivatives (WD) is presented with the aim of constructing efficient algorithms for the estimation of the “Greeks” of financial derivatives. The key idea is to replace the derivative of the probability measure of the underlying model by its WD. The WD method has the same advantageous property of the well-known score function method that the form of the Greek estimator does not depend on the details of the payoff function but only on the probability density of the underlying model. Simulation studies indicate that the WD estimator has significantly lower variance than the score function and finite difference estimator, however, the associated computational burden in certain cases may not be negligible.

Suggested Citation

  • Kloeden Peter E. & Sanz-Chacón Carlos, 2011. "Efficient price sensitivity estimation of financial derivatives by weak derivatives," Monte Carlo Methods and Applications, De Gruyter, vol. 17(1), pages 47-75, January.
    • Handle: RePEc:bpj:mcmeap:v:17:y:2011:i:1:p:47-75:n:1
    DOI: 10.1515/mcma.2011.001
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    References listed on IDEAS

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