American options from MARS

  • Authors:
  • Samuel M. T. Ehrlichman;Shane G. Henderson

  • Affiliations:
  • Cornell University, Ithaca, NY;Cornell University, Ithaca, NY

  • Venue:
  • Proceedings of the 38th conference on Winter simulation
  • Year:
  • 2006

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Abstract

We develop a class of control variates for the American option pricing problem that are constructed through the use of MARS -- multivariate adaptive regression splines. The splines approximate the option's value function at each time step, and the value function approximations are then used to construct a martingale that serves as the control variate. Significant variance reduction is possible even in high dimensions. The primary restriction is that we must be able to compute certain one-step conditional expectations.