TY - JOUR
T1 - Jumps Without Tears: A New Splitting Technology for Barrier Options
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 - <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>