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Efficient computation of option price sensitivities for options of American style


  • Wallner, Christian
  • Wystup, Uwe


No front-office software can survive without providing derivatives of option prices with respect to underlying market or model parameters, the so called Greeks. If a closed form solution for an option exists, Greeks can be computed analytically and they are numerically stable. However, for American style options, there is no closed-form solution. The price is computed by binomial trees, finite difference methods or an analytic approximation. Taking derivatives of these prices leads to instable numerics or misleading results, specially for Greeks of higher order. We compare the computation of the Greeks in various pricing methods and conclude with the recommendation to use Leisen-Reimer trees.

Suggested Citation

  • Wallner, Christian & Wystup, Uwe, 2004. "Efficient computation of option price sensitivities for options of American style," CPQF Working Paper Series 1, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
  • Handle: RePEc:zbw:cpqfwp:1

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    American options; Greeks; Leisen-Reimer trees;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • F31 - International Economics - - International Finance - - - Foreign Exchange


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