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Optimal importance sampling with explicit formulas in continuous time

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Boston University, 111 Cummington St., Boston, MA, 02215, USA

    Paolo Guasoni & Scott Robertson

Authors
  1. Paolo Guasoni
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  2. Scott Robertson
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Corresponding author

Correspondence to Paolo Guasoni.

Additional information

The authors acknowledge the support of the National Science Foundation under grants DMS-0532390 (Guasoni) and DGE-0221680 (Robertson) at Boston University.

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Guasoni, P., Robertson, S. Optimal importance sampling with explicit formulas in continuous time. Finance Stoch 12, 1–19 (2008). https://doi.org/10.1007/s00780-007-0053-5

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  • DOI: https://doi.org/10.1007/s00780-007-0053-5

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