SINH-acceleration: efficient evaluation of probability distributions, option pricing, calibration and Monte-Carlo simulations

Characteristic functions of several popular classes of distributions and processesadmit analytic continuation into unions of strips and open coni around the real hyperplane.  In the paper, we suggest to use the Fourier... [ view full abstract ]

Characteristic functions of several popular classes of distributions and processesadmit analytic continuation into unions of strips and open coni around the real hyperplane.  In the paper, we suggest to use the Fourier transform technique and changes of variables of the form $\xi=\sqrt{-1}\om_1+b\sinh (\sqrt{-1}\om+y)$ and the simplified trapezoid rule to evaluate the integrals accurately and fast. We formulate the general scheme, and apply the scheme for calculation probability distributions and pricing European options in L\'evy models, the Heston model, the CIR model, and a subordinated NTS model. We outline applications to fast and accurate calibration procedures and Monte Carlo simulations.