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Combined Derivative Estimators

In: Advances in Modeling and Simulation

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  • Paul Glasserman

    (Columbia Business School)

Abstract

We discuss combinations of simulation-based derivative estimators using infinitesimal perturbation analysis (IPA) and the likelihood ratio method (LRM). We first provide a historical perspective on combinations of IPA and LRM and then turn to connections with the generalized likelihood ratio (GLR) method. We re-derive a GLR estimator for barrier options through a combination of IPA and LRM. We then consider the behavior of a GLR estimator for a discrete-time approximation to a diffusion process as the time step shrinks. We show that an average of low-rank GLR estimators has a continuous-time limit, even though each individual estimator blows up. The limit matches an estimator previously derived through Malliavin calculus and also through a combination of IPA and LRM.

Suggested Citation

  • Paul Glasserman, 2022. "Combined Derivative Estimators," Springer Books, in: Zdravko Botev & Alexander Keller & Christiane Lemieux & Bruno Tuffin (ed.), Advances in Modeling and Simulation, pages 193-210, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-10193-9_10
    DOI: 10.1007/978-3-031-10193-9_10
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