Series Expansions and Direct Inversion for the Heston Model

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Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact distribution. We construct a new series expansion for this integral in terms of double infinite weighted sums of particular independent random variables through a change of measure and the decomposition of squared Bessel bridges. When approximated by series truncations, this representation has exponentially decaying truncation errors. We propose feasible strategies to largely reduce the implementation of the new series to simulations of simple random variables that are independent of any model parameters. We further develop direct inversion algorithms to generate samples for such random variables based on Chebyshev polynomial approximations for their inverse distribution functions. These approximations can be used under any market conditions. Thus, we establish a strong, efficient, and almost exact sampling scheme for the Heston model.
Original languageEnglish
Pages (from-to)487–549
Number of pages63
JournalSIAM Journal on Financial Mathematics
Issue number1
Publication statusPublished - 30 Mar 2021


  • Chebyshev approximation
  • Direct inversion
  • Series expansion
  • Stochastic volatility

ASJC Scopus subject areas

  • Numerical Analysis
  • Finance
  • Applied Mathematics


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