BENCHOP–SLV: The BENCHmarking project in Option Pricing–Stochastic and Local Volatility problems

Lina von Sydow, Slobodan Milovanović, Elisabeth Larsson, Karel In 't Hout, Magnus Wiktorsson, Cornelis W. Oosterlee, Victor Shcherbakov, Maarten Wyns, Alvaro Leitao, Shashi Jain, Tinne Haentjens, Johan Waldén

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
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Abstract

In the recent project BENCHOP–the BENCHmarking project in Option Pricing we found that Stochastic and Local Volatility problems were particularly challenging. Here we continue the effort by introducing a set of benchmark problems for this type of problems. Eight different methods targeted for the Stochastic Differential Equation (SDE) formulation and the Partial Differential Equation (PDE) formulation of the problem, as well as Fourier methods making use of the characteristic function, were implemented to solve these problems. Comparisons are made with respect to time to reach a certain error level in the computed solution for the different methods. The implemented Fourier method was superior to all others for the two problems where it was implemented. Generally, methods targeting the PDE formulation of the problem outperformed the methods for the SDE formulation. Among the methods for the PDE formulation the ADI method stood out as the best performing one.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalInternational Journal of Computer Mathematics
DOIs
Publication statusE-pub ahead of print - 2018

Keywords

  • 65-02
  • 91G20
  • 91G60
  • benchmark problem
  • characteristic function
  • numerical methods
  • Option pricing
  • partial differential equation
  • stochastic and local volatility
  • stochastic differential equation

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