Asymptotics of the Rough Heston Model

The recent explosion of work on rough volatility and fractional Brownian motion has led to the development of a new generation of stochastic volatility models. Such models are able to capture a wide range of stylised facts that classical models simply do not. While these models have sound mathematical underpinnings, they are difficult to implement, largely due to the fact that fractional Brownian motion is neither Markovian nor a semimartingale. One idea is to investigate the behaviour of these models as maturities become very small (or very large) and consider asymptotic estimates for quantities of interest. Here we investigate the performance of small-time asymptotic formulae for the cumulant generating function of the Fractional Heston model as presented in Guennoun et al. (2018). These formulae and their effectiveness for small-time pricing are interrogated and compared against the Rough Heston model proposed in El Euch and Rosenbaum (2019).

Grantor

Department of Finance and Tax

Year dc:date.issued

2021

Author dc:creator

• Hayes, Joshua J

Advisor dc:contributor.advisor

• Ouwehand, Peter

• Mathematical Finance

Handle dc:identifier.uri

http://hdl.handle.net/11427/35803

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/35803