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Variance Reduction

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Author
Gilles Pagès
Published in
Numerical Probability
Publisher
Springer Nature Switzerland

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Abstract

The rate of convergence of the Monte Carlo method being universal, the only way to shrink the confidence interval is to reduce its asymptotic variance by replacing the random variable of interest by another one with the same expectation but lower variance. This chapter presents the main methods to do so: static and dynamic (regression) control variate, convexity methods (Jensen's inequality), antithetic method, pre-conditioning (Blackwell-Rao), stratification and importance sampling. Various applications to the pricing of derivatives are proposed. In particular, the use of parity equations - such as the call-put parity equations -- to produce synthetic call or put payoffs with a very low variance.

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previous chapter The Monte Carlo Method and Applications to Option Pricing
next chapter The Quasi-Monte Carlo Method
Title
Variance Reduction
Author
Gilles Pagès
Copyright Year
2026
Book
Numerical Probability

Print ISBN: 978-3-032-10091-7

Electronic ISBN: 978-3-032-10092-4

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-3-032-10092-4_3

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