Markovian approximations of stochastic Volterra equations with the fractional kernel

Christian Bayer and Simon Breneis

Quantitative Finance, 2023, vol. 23, issue 1, 53-70

Abstract: We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is therefore not a Markov process or semimartingale, and has quite low Hölder-regularity. In practice, simulating such rough processes thus often results in high computational cost. To remedy this, we study approximations of stochastic Volterra equations using an N-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation. If the coefficients of the stochastic Volterra equation are Lipschitz continuous, we show that these approximations converge strongly with superpolynomial rate in N. Finally, we apply this approximation to compute the implied volatility smile of a European call option under the rough Bergomi and the rough Heston model.

Date: 2023
References: Add references at CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://hdl.handle.net/10.1080/14697688.2022.2139193 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:23:y:2023:i:1:p:53-70

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RQUF20

DOI: 10.1080/14697688.2022.2139193

Access Statistics for this article

Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral

More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().