Finance and Stochastics

, Volume 12, Issue 1, pp 1–19 | Cite as

Optimal importance sampling with explicit formulas in continuous time

  • Paolo Guasoni
  • Scott Robertson


In the Black–Scholes model, consider the problem of selecting a change of drift which minimizes the variance of Monte Carlo estimators for prices of path-dependent options.

Employing large deviations techniques, the asymptotically optimal change of drift is identified as the solution to a one-dimensional variational problem, which may be reduced to the associated Euler–Lagrange differential equation.

Closed-form solutions for geometric and arithmetic average Asian options are provided.


Monte Carlo methods Variance reduction Importance sampling Large deviations 

Mathematics Subject Classification (2000)

91B28 60F10 65C05 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBoston UniversityBostonUSA

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