The Hybrid-Exponential Scheme for Stochastic Volterra Equations

35 Pages Posted: 23 Nov 2020

See all articles by Sigurd Emil Rømer

Sigurd Emil Rømer

University of Copenhagen, Department of Mathematical Sciences

Date Written: October 22, 2020

Abstract

We present the hybrid-exponential scheme for simulating stochastic Volterra equations. The scheme is based on an exact approximation of the kernel function near the origin and an approximation by a sum of exponentials across the rest of the domain. The first part is similar to the hybrid scheme introduced in and is needed to capture any singular behavior of the kernel. The second part follows the ideas of where rough volatility models are under consideration and results in a number of stochastic factors to be simulated, one for each exponential term, and all with linear complexity in time. Since the efficiency of our scheme relies heavily on ensuring a low number of factors, we include also a review of various methods for finding the exponential terms. We here discover the method of and show that many fewer terms are needed for the rough fractional kernel than previously established in. Lastly, we provide a proof of convergence and also numerically demonstrate the efficiency of the scheme by example on the rough Bergomi model from.

Keywords: Stochastic Volterra Equations, Simulation, Stochastic Volatility, Rough Volatility, Option Pricing, Rough Bergomi

JEL Classification: C15, C63, C65, G13

Suggested Citation

Rømer, Sigurd Emil, The Hybrid-Exponential Scheme for Stochastic Volterra Equations (October 22, 2020). Available at SSRN: https://ssrn.com/abstract=3706253 or http://dx.doi.org/10.2139/ssrn.3706253

Sigurd Emil Rømer (Contact Author)

University of Copenhagen, Department of Mathematical Sciences

Universitetsparken 5
Copenhagen, København Ø 2100
Denmark

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
89
Abstract Views
725
rank
333,678
PlumX Metrics