A Black--Scholes Model with Long Memory
Pricing of Securities
2012-02-28 v1 Classical Analysis and ODEs
Dynamical Systems
Probability
Computational Finance
Abstract
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised. Connections with the class of ARCH() processes are sketched.
Keywords
Cite
@article{arxiv.1202.5574,
title = {A Black--Scholes Model with Long Memory},
author = {John A. D. Appleby and John A. Daniels and Katja Krol},
journal= {arXiv preprint arXiv:1202.5574},
year = {2012}
}
Comments
John Appleby and John Daniels were partially funded by the Science Foundation Ireland grant 07/MI/008 "Edgeworth Centre for Financial Mathematics". John Daniels was also partially funded by The Embark Initiative operated by the Irish Research Council for Science, Engineering and Technology (IRCSET) under the project "Volatility Models in Inefficient Markets". Katja Krol was supported by the Deutsche Telekom Stiftung