Gero Junike

Ludwig-Maximilians-Universität (LMU) München

Title

Exact simulation of stochastic volatility models based on conditional Fourier-cosine method

Authors

Riccardo Brignone and Gero Junike

Abstract

The traditional methodology used for the exact simulation of stochastic volatility models based on the Gil-Pelaez formula presents implementation problems that are observed by many researchers and practitioners. In particular, although conventionally considered exact, such a method presents a difficult control of the error. The bias of the Monte Carlo simulation estimator can only be computed numerically and is controlled by two parameters, typically determined by running time-consuming simulations under different tuning parameter configurations until an optimal setup is found. In this paper, we propose a new exact simulation scheme based on the Fourier-cosine method, which approximates a probability density given the characteristic function as follows: the density is truncated on a finite interval, and approximated by a classical Fourier-cosine series. The method allows full error control via an effective automatic identification of the tuning parameters given a user-supplied error tolerance. The new approach offers the following advantages: improved control of the error, simplified implementation, and reduction in computing time. The error is controlled by only one parameter instead of two. This parameter has a clear interpretation: it is the maximum tolerable bias. This facilitates the implementation, since the maximum bias becomes an input of the simulation algorithm, instead of an output, and can be set a priori, before running simulations. Our analysis shows that the proposed exact simulation scheme is computationally faster than the traditional one, and presents an improved speed-accuracy profile with respect to alternative state-of-the-art fast approximated sampling schemes.