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We analyze the qualitative differences between prices of double barrierno-touch options in the Heston model and pure jump KoBoL model calibrated tothe same set of the empirical data, and discuss the potential for arbitrageopportunities if the correct model is a pure jump model. We explain anddemonstrate with numerical examples that accurate and fast calculations ofprices of double barrier options in jump models are extremely difficult usingthe numerical methods available in the literature. We develop a new efficientmethod (GWR-SINH method) based of the Gaver-Wynn-Rho acceleration applied tothe Bromwich integral; the SINH-acceleration and simplified trapezoid rule areused to evaluate perpetual double barrier options for each value of thespectral parameter in GWR-algorithm. The program in Matlab running on a Macwith moderate characteristics achieves the precision of the order of E-5 andbetter in several several dozen of milliseconds; the precision E-07 isachievable in about 0.1 sec. We outline the extension of GWR-SINH method toregime-switching models and models with stochastic parameters and stochasticinterest rates.

Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models