Jumps without tears: A new splitting technology for barrier options

Andrey Itkin, Peter Carr

Research output: Contribution to journalArticlepeer-review

Abstract

The market pricing of OTC FX options displays both stochastic volatility and stochastic skewness in the risk-neutral distribution governing currency returns. To capture this unique phenomenon Carr and Wu developed a model (SSM) with three dynamical state variables. They then used Fourier methods to value simple European-style options. However pricing exotic options requires numerical solution of 3D unsteady PIDE with mixed derivatives which is expensive. In this paper to achieve this goal we propose a new splitting technique. Being combined with another method of the authors, which uses pseudo-parabolic PDE instead of PIDE, this reduces the original 3D unsteady problem to a set of 1D unsteady PDEs, thus allowing a significant computational speedup. We demonstrate this technique for single and double barrier options priced using the SSM.

Original languageEnglish (US)
Pages (from-to)667-704
Number of pages38
JournalInternational Journal of Numerical Analysis and Modeling
Volume8
Issue number4
StatePublished - 2011

Keywords

  • Barrier options
  • Finite-difference scheme
  • General stable tempered process
  • Jump-diffusion
  • Numerical method
  • Pricing
  • Stochastic skew
  • The Green function

ASJC Scopus subject areas

  • Numerical Analysis

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