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Volume 8, Issue 4
Jumps Without Tears: A New Splitting Technology for Barrier Options

A. Itkin & P. Carr

Int. J. Numer. Anal. Mod., 8 (2011), pp. 667-704.

Published online: 2011-08

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  • 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.

  • Keywords

Barrier options, pricing, stochastic skew, jump-diffusion, finite-difference scheme, numerical method, the Green function, general stable tempered process.

  • AMS Subject Headings

60J75, 35M99, 65L12, 65L20, 34B27, 65T50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-667, author = {A. Itkin and P. Carr}, title = {Jumps Without Tears: A New Splitting Technology for Barrier Options}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {4}, pages = {667--704}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/706.html} }
TY - JOUR T1 - Jumps Without Tears: A New Splitting Technology for Barrier Options AU - A. Itkin & P. Carr JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 667 EP - 704 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/706.html KW - Barrier options, pricing, stochastic skew, jump-diffusion, finite-difference scheme, numerical method, the Green function, general stable tempered process. AB -

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.

A. Itkin and P. Carr. (2011). Jumps Without Tears: A New Splitting Technology for Barrier Options. International Journal of Numerical Analysis and Modeling. 8 (4). 667-704. doi:
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