Jump Without Tears: a New Splitting Technology for Barrier Options
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@Article{IJNAM-8-667,
author = {A. Itkin and P. Carr},
title = {Jump 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 - Jump 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
KW - pricing
KW - stochastic skew
KW - jump-diffusion
KW - finite-difference scheme
KW - numerical method
KW - the Green function
KW - 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 & P. Carr. (1970). Jump 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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