Pricing American options with the Runge-Kutta-Legendre finite difference scheme

Fabien Le Floc'h

Research output: Contribution to journalArticleScientificpeer-review


This paper presents the Runge-Kutta-Legendre (RKL) finite difference scheme, allowing for an additional shift in its polynomial representation. A short presentation of the stability region, comparatively to the Runge-Kutta-Chebyshev scheme follows. We then explore the problem of pricing American options with the RKL scheme under the one factor Black-Scholes and the two factor Heston stochastic volatility models, as well as the pricing of butterfly spread and digital options under the uncertain volatility model, where a Hamilton-Jacobi-Bellman partial differential equation needs to be solved. We explore the order of convergence in these problems, as well as the option greeks stability, compared to the literature and popular schemes such as Crank-Nicolson, with Rannacher time-stepping.

Original languageEnglish
Article number2150018
Number of pages1
JournalInternational Journal of Theoretical and Applied Finance
Issue number3
Publication statusPublished - 2021


  • American options
  • finite difference method
  • pricing
  • quantitative finance
  • Runge-Kutta-Chebyshev
  • Runge-Kutta-Legendre
  • stochastic volatility
  • uncertain volatility


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