A note on the discontinuity problem in Heston's stochastic volatility model

Jia-Hau Guo*, Mao Wei Hung

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Although quasi-analytic formulas can be derived for European-style financial claims in Heston's stochastic volatility model, the inverse Fourier integration involved makes the calculation somewhat complicated. This challenge has puzzled practitioners for many years because most implementations of Heston's formula are not robust, even for customarily-used Heston parameters, as time to maturity is increased. In this article, a simplified approach is proposed to solve the numerical instability problem inherent to the fundamental solution of the Heston model. Specifically, the solution does not require any additional function or a particular mechanism for most software packages or programming library routines to correctly evaluate Heston's analytics.

Original languageEnglish
Pages (from-to)339-345
Number of pages7
JournalApplied Mathematical Finance
Issue number4
StatePublished - 1 Sep 2007


  • Discountinuity
  • Heston
  • Options
  • Stochastic volatility model

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