@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 = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/706.html}
}