# Sinh-Acceleration: Efficient Evaluation of Probability Distributions, Option Pricing, and Monte-Carlo Simulations

39 Pages Posted: 5 Mar 2018 Last revised: 9 May 2018

See all articles by Svetlana Boyarchenko

## Svetlana Boyarchenko

University of Texas at Austin - Department of Economics

## Sergei Levendorskii

Calico Science Consulting

Date Written: February 25, 2018

### Abstract

Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around the line of integration in the complex plane.

The Fourier transform techniques reduces calculation of probability distributions and option prices to evaluation of integrals whose integrands are analytic in domains enjoying these properties.

In the paper, we suggest to use changes of variables of the form $\xi=\sqrt{-1}\omega_1 b\sinh (\sqrt{-1}\omega y)$ 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 Lévy 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.

Keywords: sinh-regular Lévy processes, sinh-regular distributions, sinh-acceleration, Heston model, KoBoL, CGMY, CIR, CIR subordinator, Monte-Carlo simulations

JEL Classification: C63

Suggested Citation

Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., Sinh-Acceleration: Efficient Evaluation of Probability Distributions, Option Pricing, and Monte-Carlo Simulations (February 25, 2018). Available at SSRN: https://ssrn.com/abstract=3129881 or http://dx.doi.org/10.2139/ssrn.3129881